2025

• Li, Junjian; Zhao, Lin; Møyner, Olav; Lie, Knut-Andreas. (2025) A new near-wellbore modeling method for deviated wells incorner-point grid. Advances in Geo-Energy Research
  Academic article

2024

• Lie, Knut-Andreas; Møyner, Olav; Klemetsdal, Øystein; Skaflestad, Bård; Moncorgé, Arthur; Kippe, Vegard. (2024) Enhancing performance of complex reservoir models via convergence monitors.
  Academic chapter/article/Conference paper
• Rasmussen, Atgeirr Flø; Møyner, Olav; Skaflestad, Bård; Lie, Knut-Andreas; Torben, Jakob; Moncorgé, Arthur. (2024) Distributed Field-Scale Parallel Nonlinear Domain Decomposition Solver.
  Academic chapter/article/Conference paper
• Nordbotten, Jan Martin; Fernø, Martin; Flemisch, Bernd; Kovscek, Anthony R.; Lie, Knut-Andreas. (2024) The 11th Society of Petroleum Engineers Comparative Solution Project: Problem Definition. SPE Journal
  Academic article
• Xiong, Wei; Zhang, Lie-Hui; Zhao, Yu-Long; Wen, Shao-Mu; Bao, Kai; Møyner, Olav. (2024) Compositional Simulation for Carbon Storage in Porous Media Using an Electrolyte Association Equation of State. SPE Journal
  Academic article
• Saló-Salgado, Lluís; Møyner, Olav; Lie, Knut-Andreas; Juanes, Ruben. (2024) Three-dimensional simulation of geologic carbon dioxide sequestration using MRST. Advances in Geo-Energy Research
  Academic article
• Aslam, Billal; Yan, Bicheng; Lie, Knut-Andreas; Krogstad, Stein; Møyner, Olav; He, Xupeng. (2024) A Novel Hybrid Physics/Data-Driven Model for Fractured Reservoir Simulation. SPE Journal
  Academic article

2023

• Aslam, Billal; Yan, Bicheng; Tariq, Zeeshan; Krogstad, Stein; Lie, Knut-Andreas. (2023) Rapid Simulation and Optimization of Geological CO2 Sequestration Using Coarse Grid Network Model.
  Academic chapter/article/Conference paper
• Lie, Knut-Andreas; Krogstad, Stein. (2023) Data-driven modelling with coarse-grid network models. Computational Geosciences
  Academic article
• Møyner, Olav; Rasmussen, Atgeirr Flø; Klemetsdal, Øystein; Nilsen, Halvor Møll; Moncorgé, Arthur; Lie, Knut-Andreas. (2023) Nonlinear domain-decomposition preconditioning for robust and efficient field-scale simulation of subsurface flow. Computational Geosciences
  Academic article
• Lie, Knut-Andreas; Møyner, Olav; Klemetsdal, Øystein. (2023) An Adaptive Newton–ASPEN Solver for Complex Reservoir Models.
  Academic chapter/article/Conference paper
• Krogstad, Stein; Klemetsdal, Øystein; Lie, Knut-Andreas. (2023) Efficient Adaptation and Calibration of Ad joint-Based Reduced-Order Coarse-Grid Network Models.
  Academic chapter/article/Conference paper
• Liu, Hui; Liao, Xinwei; Lie, Knut-Andreas; Klemetsdal, Øystein; Bao, Kai; Zhang, Xiaoliang. (2023) An Integrated Modeling Framework for Simulating Complex Transient Flow in Fractured Reservoirs with 3D High-Quality Grids.
  Academic chapter/article/Conference paper

2022

• Lie, Knut-Andreas; Krogstad, Stein. (2022) Comparison of two different types of reduced graph-based reservoir models: Interwell networks (GPSNet) versus aggregated coarse-grid networks (CGNet). Journal of Petroleum Science and Engineering
  Academic article
• Lie, Knut-Andreas; Krogstad, Stein. (2022) Data-Driven Modelling with Coarse-Grid Network Models.
  Academic chapter/article/Conference paper
• Møyner, Olav; Rasmussen, Atgeirr Flø; Klemetsdal, Øystein; Nilsen, Halvor Møll; Arthur, Moncorgé; Lie, Knut-Andreas. (2022) Nonlinear Domain Decomposition Preconditioning for Robust and Efficient Field-Scale Simulation of Subsurface Flow.
  Academic chapter/article/Conference paper
• Oliveira, Gustavo P.; Rodrigues, Thiago N. E.; Lie, Knut-Andreas. (2022) GAWPS: A MRST-based module for wellbore profiling and graphical analysis of flow units. Advances in Geo-Energy Research
  Academic article
• Andersen, Odd; Lie, Knut-Andreas; Rao, Samvith. (2022) Getting Into Reservoir Modeling for Carbon Sequestration. The Way Ahead
  Popular scientific article
• Kvamsdal, Trond; Mathisen, Kjell Magne; Lie, Knut-Andreas; Larson, Mats G.. (2022) 8th European Congress on Computational Methods in Applied Sciences and Engineering (ECCOMAS Congress 2022). European Community on Computional Methods in Applied Sciences (ECCOMAS) European Community on Computional Methods in Applied Sciences (ECCOMAS)
  Academic anthology/Conference proceedings

2021

• Klemetsdal, Øystein Strengehagen; Lie, Knut-Andreas. (2021) Implicit Discontinuous Galerkin Methods for Transport Equations in Porous Media.
  Academic chapter/article/Conference paper
• Lie, Knut-Andreas; Møyner, Olav. (2021) Multiscale Pressure Solvers for Stratigraphic and Polytopal Grids.
  Academic chapter/article/Conference paper
• Lie, Knut-Andreas; Møyner, Olav. (2021) Advanced Modeling with the MATLAB Reservoir Simulation Toolbox. Cambridge University Press Cambridge University Press
  Academic anthology/Conference proceedings
• Sun, Xin; Lie, Knut-Andreas; Bao, Kai. (2021) Using State Functions and MRST’s AD-OO Framework to Implement Simulators for Chemical EOR.
  Academic chapter/article/Conference paper
• Berge, Runar Lie; Klemetsdal, Øystein Strengehagen; Lie, Knut-Andreas. (2021) Unstructured PEBI Grids Conforming to Lower-Dimensional Objects.
  Academic chapter/article/Conference paper
• Klemetsdal, Øystein Strengehagen; Møyner, Olav; Moncorgé, Arthur; Nilsen, Halvor Møll; Lie, Knut-Andreas. (2021) High-Resolution Compositional Reservoir Simulation with Dynamic Coarsening and Local Timestepping for Unstructured Grids. SPE Journal
  Academic article
• Klemetsdal, Øystein Strengehagen; Moncorgé, Arthur; Møyner, Olav; Lie, Knut-Andreas. (2021) A numerical study of the additive Schwarz preconditioned exact Newton method (ASPEN) as a nonlinear preconditioner for immiscible and compositional porous media flow. Computational Geosciences
  Academic article
• Klemetsdal, Øystein Strengehagen; Moncorgé, Arthur; Nilsen, Halvor Møll; Møyner, Olav; Lie, Knut-Andreas. (2021) An adaptive sequential fully implicit domain-decomposition solver. SPE Journal
  Academic article
• Reveron, Manuel Antonio Borregales; Holm, Håvard Heitlo; Møyner, Olav; Krogstad, Stein; Lie, Knut-Andreas. (2021) Numerical Comparison Between ES-MDA and Gradient-Based Optimization for History Matching of Reduced Reservoir Models.
  Academic chapter/article/Conference paper
• Raynaud, Xavier; Pizzolato, Alberto; Johansson, August; Caresani, Federica; Ferrari, Andrea; Møyner, Olav. (2021) Toward accurate reservoir simulations on unstructured grids: design of simple error estimators and critical benchmarking of consistent discretization methods for practical implementation. SPE Journal
  Academic article
• Ma, Shuai; Ju, Binshan; Zhao, Lin; Lie, Knut-Andreas; Dong, Yintao; Zhang, Qilong. (2021) Embedded discrete fracture modeling: flow diagnostics, non-Darcy flow, and well placement optimization. Journal of Petroleum Science and Engineering
  Academic article
• Watson, Francesca; Krogstad, Stein; Lie, Knut-Andreas. (2021) The use of flow diagnostics to rank model ensembles. Computational Geosciences
  Academic article
• Lie, Knut-Andreas; Møyner, Olav. (2021) Preface.
  Introduction

2020

• Reveron, Manuel Antonio Borregales; Møyner, Olav; Krogstad, Stein; Lie, Knut-Andreas. (2020) Data-Driven Models Based on Flow Diagnostics.
  Academic chapter/article/Conference paper
• Watson, Francesca; Krogstad, Stein; Lie, Knut-Andreas. (2020) Flow diagnostics for model ensembles.
  Academic chapter/article/Conference paper
• Klemetsdal, Øystein Strengehagen; Lie, Knut-Andreas. (2020) Dynamic Coarsening and Local Reordered Nonlinear Solvers for Simulating Transport in Porous Media. SPE Journal
  Academic article
• Lie, Knut-Andreas; Krogstad, Stein; Watson, Francesca. (2020) User Guide to Flow Diagnostics Postprocessing - Simulations in MRST and ECLIPSE Output Format. SINTEF Digital SINTEF Digital
  Report
• Linga, Gaute; Møyner, Olav; Nilsen, Halvor Møll; Arthur, Moncorgé; Lie, Knut-Andreas. (2020) An implicit local time-stepping method based on cell reordering for multiphase flow in porous media. Journal of Computational Physics: X
  Academic article
• Nilsen, Halvor Møll; Arthur, Moncorgé; Bao, Kai; Møyner, Olav; Lie, Knut-Andreas; Brodtkorb, Andre. (2020) Comparison between algebraic multigrid and multilevel multiscale methods for reservoir simulation.
  Academic chapter/article/Conference paper
• Klemetsdal, Øystein Strengehagen; Moncorgé, Arthur; Møyner, Olav; Lie, Knut-Andreas. (2020) Additive Schwarz Preconditioned Exact Newton Method as a Nonlinear Preconditioner for Multiphase Porous Media Flow.
  Academic chapter/article/Conference paper
• Klemetsdal, Øystein Strengehagen; Møyner, Olav; Raynaud, Xavier; Lie, Knut-Andreas. (2020) A Comparison of Consistent Discretizations for Elliptic Problems on Polyhedral Grids.
  Academic chapter/article/Conference paper
• Rasmussen, Atgeirr Flø; Sandve, Tor Harald; Bao, Kai; Lauser, Andreas; Hove, Joakim; Skaflestad, Bård. (2020) The Open Porous Media Flow Reservoir Simulator. Computers and Mathematics with Applications
  Academic article
• Holm, Håvard Heitlo; Lie, Knut-Andreas; Brodtkorb, André R.; Sætra, Martin Lilleeng. (2020) Efficient Forecasting of Drift Trajectories using Simplified Ocean Models and Nonlinear Data Assimilation on GPUs. Norges teknisk-naturvitenskapelige universitet Norges teknisk-naturvitenskapelige universitet
  Doctoral dissertation
• Lie, Knut-Andreas; Krogstad, Stein; Watson, Francesca; Reveron, Manuel Antonio Borregales. (2020) User Guide to Flow Diagnostics in MRST - Flow Diagnostics Preprocessors for Model Ensembles. SINTEF Digital SINTEF Digital
  Report

2019

• Guion, Alexandre Nicolas; Skaflestad, Bård; Lie, Knut-Andreas; Wu, Xiao-Hui. (2019) Validation of a non-uniform coarsening and upscaling framework.
  Academic chapter/article/Conference paper
• Klemetsdal, Øystein; Møyner, Olav; Lie, Knut-Andreas. (2019) Implicit high-resolution compositional simulation with optimal ordering of unknowns and adaptive spatial refinement.
  Academic chapter/article/Conference paper
• Marefat, Hassan Ali; Aghdam, Muhammad A Ashjari; Lie, Knut-Andreas. (2019) Preserving vorticity improves the accuracy of multiscale solvers. Journal of Petroleum Science and Engineering
  Academic article
• Klemetsdal, Øystein Strengehagen; Rasmussen, Atgeirr Flø; Møyner, Olav; Lie, Knut-Andreas. (2019) Efficient reordered nonlinear Gauss–Seidel solvers with higher order for black-oil models. Computational Geosciences
  Academic article
• Klemetsdal, Øystein; Møyner, Olav; Lie, Knut-Andreas. (2019) Robust nonlinear Newton solver with adaptive interface-localized trust regions. SPE Journal
  Academic article
• Lie, Knut-Andreas. (2019) An Introduction to Reservoir Simulation Using MATLAB/GNU Octave: User Guide for the MATLAB Reservoir Simulation Toolbox (MRST). Cambridge University Press Cambridge University Press
  Academic monograph
• Klemetsdal, Øystein; Møyner, Olav; Lie, Knut-Andreas. (2019) Accelerating multiscale simulation of complex geomodels by use of dynamically adapted basis functions. Computational Geosciences
  Academic article
• Lie, Knut-Andreas; Mykkeltvedt, Trine Solberg; Møyner, Olav. (2019) A fully implicit WENO scheme on stratigraphic and unstructured polyhedral grids. Computational Geosciences
  Academic article
• Klemetsdal, Øystein Strengehagen; Lie, Knut-Andreas; Møyner, Olav; Raynaud, Xavier; Holden, Helge. (2019) Efficient Solvers for Field-Scale Simulation of Flow and Transport in Porous Media. Norges teknisk-naturvitenskapelige universitet Norges teknisk-naturvitenskapelige universitet
  Doctoral dissertation
• Lie, Knut-Andreas. (2019) Executive summary. SPE Journal
  Editorial
• Lie, Knut-Andreas. (2019) Executive summary. SPE Journal
  Editorial

2018

• Lie, Knut-Andreas. (2018) On Holden's seven guidelines for scientific computing and development of open-source community software.
  Academic chapter/article/Conference paper
• Lie, Knut-Andreas; Mykkeltvedt, Trine Solberg; Møyner, Olav. (2018) Fully implicit WENO schemes on stratigraphic and fully unstructured grids.
  Academic chapter/article/Conference paper
• Allen, Rebecca; Nilsen, Halvor Møll; Lie, Knut-Andreas; Møyner, Olav; Andersen, Odd. (2018) Using simplified methods to explore the impact of parameter uncertainty on CO2 storage estimates with application to the Norwegian Continental Shelf. International Journal of Greenhouse Gas Control
  Academic article
• Lie, Knut-Andreas. (2018) Executive summary. SPE Journal
  Editorial
• Lie, Knut-Andreas. (2018) Executive summary. SPE Journal
  Editorial
• Zefreh, Masoud Ghaderi; Nilsen, Halvor Møll; Lie, Knut-Andreas; Raynaud, Xavier; Doster, Florian. (2018) Streamline simulation of a reactive advective flow with discontinuous flux function. Computational Geosciences
  Academic article
• Toft, Raymond; Lie, Knut-Andreas; Møyner, Olav. (2018) Full Approximation Scheme for Reservoir Simulation. NIKT: Norsk IKT-konferanse for forskning og utdanning
  Academic article
• Klemetsdal, Øystein; Rasmussen, Atgeirr Flø; Møyner, Olav; Lie, Knut-Andreas. (2018) Nonlinear Gauss-Seidel solvers with higher order for black-oil models.
  Academic chapter/article/Conference paper
• Klemetsdal, Øystein; Møyner, Olav; Lie, Knut-Andreas. (2018) Use of dynamically adapted basis functions to accelerate multiscale simulation of complex geomodels.
  Academic chapter/article/Conference paper
• Berge, Runar Lie; Klemetsdal, Øystein; Lie, Knut-Andreas. (2018) Unstructured Voronoi grids conforming to lower-dimensional objects. Computational Geosciences
  Academic article
• Lie, Knut-Andreas. (2018) Executive summary. SPE Journal
  Editorial

2017

• Klemetsdal, Øystein; Møyner, Olav; Lie, Knut-Andreas. (2017) Non-linear Newton Solver for a Polymer Two-phase System Using Interface-localized Trust Regions.
  Academic chapter/article/Conference paper
• Lie, Knut-Andreas; Møyner, Olav; Natvig, Jostein Roald; Kozlova, Antonina; Bratvedt, Kyrre; Watanabe, Shingo. (2017) Successful application of multiscale methods in a real reservoir simulator environment. Computational Geosciences
  Academic article
• Bao, Kai; Lie, Knut-Andreas; Møyner, Olav; Liu, Ming. (2017) Fully implicit simulation of polymer flooding with MRST. Computational Geosciences
  Academic article
• Nilsen, Halvor Møll; Krogstad, Stein; Andersen, Odd; Allen, Rebecca; Lie, Knut-Andreas. (2017) Using sensitivities and vertical-equilibrium models for parameter estimation of CO2 injection models with application to Sleipner data. Energy Procedia
  Academic article
• Lie, Knut-Andreas. (2017) Executive summary. SPE Journal
  Editorial
• Lie, Knut-Andreas. (2017) Executive summary. SPE Journal
  Editorial
• Lie, Knut-Andreas. (2017) Executive summary. SPE Journal
  Editorial
• Allen, Rebecca; Nilsen, Halvor Møll; Andersen, Odd; Lie, Knut-Andreas. (2017) Ranking and categorizing large-scale saline aquifer formations based on optimized CO2 storage potentials and economic factors. International Journal of Greenhouse Gas Control
  Academic article
• Mykkeltvedt, Trine Solberg; Raynaud, Xavier; Lie, Knut-Andreas. (2017) Fully implicit higher-order schemes applied to polymer flooding. Computational Geosciences
  Academic article
• Allen, Rebecca; Nilsen, Halvor Møll; Andersen, Odd; Lie, Knut-Andreas. (2017) Categorization of Norwegian Continental Shelf formations in terms of geological CO2 storage potentials. Energy Procedia
  Academic article
• Krogstad, Stein; Lie, Knut-Andreas; Nilsen, Halvor Møll; Berg, Carl Fredrik; Kippe, Vegard. (2017) Efficient flow diagnostics proxies for polymer flooding. Computational Geosciences
  Academic article
• Lie, Knut-Andreas; Møyner, Olav; Natvig, Jostein Roald. (2017) Use of multiple multiscale operators to accelerate simulation of complex geomodels. SPE Journal
  Academic article
• Lie, Knut-Andreas; Kedia, Kushal; Skaflestad, Bård; Wang, Xioachen; Yang, Yahan; Wu, Xiao-Hui. (2017) A General Non-Uniform Coarsening and Upscaling Framework for Reduced-Order Modeling.
  Chapter
• Lie, Knut-Andreas; Møyner, Olav; Natvig, Jostein Roald. (2017) A Feature-Enriched Multiscale Method for Simulating Complex Geomodels.
  Chapter
• Klemetsdal, Øystein; Berge, Runar Lie; Lie, Knut-Andreas; Nilsen, Halvor Møll; Møyner, Olav. (2017) Unstructured Gridding and Consistent Discretizations for Reservoirs with Faults and Complex Wells.
  Academic chapter/article/Conference paper
• Vink, Jeroen; Klie, Hektor; Austin, Andy; Beckner, Brett; Bratvedt, Kyrre; Cao, Hui. (2017) SPE Reservoir Simulation Conference, 20-22 February, Montgomery, Texas, USA. Society of Petroleum Engineers Society of Petroleum Engineers
  Academic anthology/Conference proceedings
• Allen, Rebecca; Nilsen, Halvor Møll; Andersen, Odd; Lie, Knut-Andreas. (2017) On obtaining optimal well rates and placement for CO2 storage. Computational Geosciences
  Academic article

2016

• Raynaud, Xavier; Lie, Knut-Andreas; Nilsen, Halvor Møll; Rasmussen, Atgeirr Flø. (2016) The single-cell transport problem for two-phase flow with polymer. Computational Geosciences
  Academic article
• Møyner, Olav; Lie, Knut-Andreas. (2016) A multiscale restriction-smoothed basis method for compressible black-oil models. SPE Journal
  Academic article
• Lie, Knut-Andreas. (2016) Executive summary. SPE Journal
  Editorial
• Krogstad, Stein; Lie, Knut-Andreas; Nilsen, Halvor Møll; Berg, Carl Fredrik; Kippe, Vegard. (2016) Flow diagnostics for optimal polymer injection strategies.
  Academic chapter/article/Conference paper
• Hilden, Sindre Tonning; Møyner, Olav; Lie, Knut-Andreas; Bao, Kai. (2016) Multiscale simulation of polymer flooding with shear effects. Transport in Porous Media
  Academic article
• Bao, Kai; Lie, Knut-Andreas; Møyner, Olav; Liu, Ming. (2016) Fully Implicit Simulation of Polymer Flooding with MRST.
  Academic chapter/article/Conference paper
• Lie, Knut-Andreas; Mykkeltvedt, Trine Solberg; Raynaud, Xavier. (2016) Fully Implicit Higher-order Schemes Applied to Polymer Flooding.
  Academic chapter/article/Conference paper
• Lie, Knut-Andreas. (2016) Executive summary. SPE Journal
  Editorial
• Lie, Knut-Andreas; Møyner, Olav; Natvig, Jostein Roald; Antonina, Kozlova; Bratvedt, Kyrre; Watanabe, S. (2016) Successful Application of Multiscale Methods in a Real Reservoir Simulator Environment.
  Academic chapter/article/Conference paper
• Allen, Rebecca; Nilsen, Halvor Møll; Andersen, Odd; Lie, Knut-Andreas. (2016) On Obtaining Optimal Well Rates and Placement for CO2 Storage.
  Academic chapter/article/Conference paper
• Shah, Swej; Møyner, Olav; Tene, Matei; Lie, Knut-Andreas; Hajibeygi, Hadi. (2016) The multiscale restriction smoothed basis method for fractured porous media (F-MsRSB). Journal of Computational Physics
  Academic article
• Lie, Knut-Andreas. (2016) Executive summary. SPE Journal
  Editorial
• Møyner, Olav; Holden, Helge; Lie, Knut-Andreas; Natvig, Jostein Roald. (2016) Next Generation Multiscale Methods for Reservoir Simulation. Norges teknisk-naturvitenskapelige universitet Norges teknisk-naturvitenskapelige universitet
  Doctoral dissertation
• Møyner, Olav; Lie, Knut-Andreas. (2016) A multiscale restriction-smoothed basis method for high contrast porous media represented on unstructured grids. Journal of Computational Physics
  Academic article
• Andersen, Odd; Lie, Knut-Andreas; Nilsen, Halvor Møll. (2016) An Open-Source Toolchain for Simulation and Optimization of Aquifer-Wide CO2 Storage. Energy Procedia
  Academic article

2015

• Dragland, Åse Kirsti; Brodtkorb, André R.; Rasmussen, Atgeirr Flø; Lie, Knut-Andreas. (2015) Nytt språk gir kjappe simuleringer. Gemini
  Popular scientific article
• Nilsen, Halvor Møll; Lie, Knut-Andreas; Andersen, Odd. (2015) Analysis of CO2 trapping capacities and long-term migration for geological formations in the Norwegian North Sea using MRST-co2lab. Computers & Geosciences
  Academic article
• Krogstad, Stein; Lie, Knut-Andreas; Møyner, Olav; Nilsen, Halvor Møll; Raynaud, Xavier; Skaflestad, Bård. (2015) MRST-AD: an open-source framework for rapid prototyping and evaluation of reservoir simulation problems.
  Academic chapter/article/Conference paper
• Lie, Knut-Andreas; Møyner, Olav; Krogstad, Stein. (2015) Application of Flow Diagnostics and Multiscale Methods for Reservoir Management.
  Academic chapter/article/Conference paper
• Møyner, Olav; Lie, Knut-Andreas. (2015) A multiscale method based on restriction-smoothed basis functions suitable for general grids in high contrast media.
  Academic chapter/article/Conference paper
• Nilsen, Halvor Møll; Lie, Knut Andreas; Møyner, Olav; Andersen, Odd. (2015) Spill-point analysis and structural trapping capacity in saline aquifers using MRST-co2lab. Computers & Geosciences
  Academic article
• Nilsen, Halvor Møll; Lie, Knut-Andreas; Andersen, Odd. (2015) Robust simulation of sharp-interface models for fast estimation of CO2 trapping capacity in large-scale aquifer systems. Computational Geosciences
  Academic article
• Pal, Mayur; Lamine, Sadok; Lie, Knut Andreas; Krogstad, Stein. (2015) Validation of the multiscale mixed finite-element method. International Journal for Numerical Methods in Fluids
  Academic article
• Lie, Knut-Andreas; Mallison, Bradley T.. (2015) Mathematical models for oil reservoir simulation.
  Encyclopedia article
• Lie, Knut-Andreas. (2015) Hyperbolic Conservation Laws: Computation.
  Encyclopedia article
• Nilsen, Halvor Møll; Lie, Knut-Andreas; Andersen, Odd. (2015) Fully-implicit simulation of vertical-equilibrium models with hysteresis and capillary fringe. Computational Geosciences
  Academic article
• Lie, Knut-Andreas; Nilsen, Halvor Møll; Andersen, Odd; Møyner, Olav. (2015) A simulation workflow for large-scale CO2 storage in the Norwegian North Sea. Computational Geosciences
  Academic article
• Kaulmann, Sven; Flemisch, Bernd; Haasdonk, Bernard; Lie, Knut-Andreas; Ohlberger, Mario. (2015) The localized reduced basis multiscale method for two-phase flows in porous media. International Journal for Numerical Methods in Engineering
  Academic article
• Nilsen, Halvor Møll; Lie, Knut-Andreas; Andersen, Odd. (2015) Analysis of CO2 trapping capacities and long-term migration for geological formations in the Norwegian North Sea using MRST-CO2LAB. Petroleum Abstracts (PA)
  Abstract
• Sætra, Martin Lilleeng; Brodtkorb, André R.; Lie, Knut Andreas. (2015) Efficient GPU-Implementation of Adaptive Mesh Refinement for the Shallow-Water Equations. Journal of Scientific Computing
  Academic article

2014

• Møyner, Olav; Lie, Knut Andreas. (2014) A multiscale two-point flux-approximation method. Journal of Computational Physics
  Academic article
• Møyner, Olav; Krogstad, Stein; Lie, Knut-Andreas. (2014) The application of flow diagnostics for reservoir management. SPE Journal
  Academic article
• Lie, Knut Andreas; Nilsen, Halvor Møll; Rasmussen, Atgeirr Flø; Raynaud, Xavier. (2014) Fast Simulation of Polymer Injection in Heavy-Oil Reservoirs on the Basis of Topological Sorting and Sequential Splitting. SPE Journal
  Academic article
• Lie, Knut Andreas; Natvig, Jostein Roald; Krogstad, Stein; Yang, Yahan; Wu, Xiao-Hui. (2014) Grid adaptation for the Dirichlet-Neumann representation method and the multiscale mixed finite-element method. Computational Geosciences
  Academic article
• Mykkeltvedt, Trine; Aavatsmark, Ivar; Lie, Knut-Andreas. (2014) Numerical Aspects of Polymer Flood Modeling.
  Academic chapter/article/Conference paper
• Andersen, Odd; Nilsen, Halvor Møll; Lie, Knut-Andreas. (2014) Reexamining CO2 Storage Capacity and Utilization of the Utsira Formation.
  Academic chapter/article/Conference paper
• Møyner, Olav; Lie, Knut Andreas. (2014) The Multiscale Finite-Volume Method on Stratigraphic Grids. SPE Journal
  Academic article
• Hilden, Sindre Kristensen; Lie, Knut-Andreas; Raynaud, Xavier. (2014) Steady State Upscaling of Polymer Flooding.
  Academic chapter/article/Conference paper
• Raynaud, Xavier; Lie, Knut-Andreas; Nilsen, Halvor Møll; Rasmussen, Atgeirr Flø. (2014) Well-posedness of the Single-cell Transport Problem for Two-phase Flow with Polymer.
  Academic chapter/article/Conference paper
• Lie, Knut-Andreas; Nilsen, Halvor Møll; Andersen, Odd; Møyner, Olav. (2014) A Simulation Workflow for Large-scale CO2 Storage in the Norwegian North Sea.
  Academic chapter/article/Conference paper
• Rasmussen, Atgeirr Flø; Lie, Knut-Andreas. (2014) Discretization of Flow Diagnostics on Stratigraphic and Unstructured Grids.
  Academic chapter/article/Conference paper

2013

• Lie, Knut Andreas; Nilsen, Halvor Møll; Rasmussen, Atgeirr Flø; Raynaud, Xavier. (2013) Fast Simulation of Polymer Injection in Heavy-Oil Reservoirs Based on Topological Sorting and Sequential Splitting.
  Academic chapter/article/Conference paper
• Møyner, Olav; Lie, Knut Andreas. (2013) The multiscale finite volume method on unstructured grids.
  Academic chapter/article/Conference paper
• Pal, Mayur; Lamine, Sadok; Lie, Knut Andreas; Krogstad, Stein. (2013) Multiscale method for simulating two and three-phase flow in porous media.
  Academic chapter/article/Conference paper

2012

• Alpak, Faruk Omer; Pal, Mayur; Lie, Knut-Andreas. (2012) A Multiscale Adaptive Local-Global Method for Modeling Flow in Stratigraphically Complex Reservoirs. SPE Journal
  Academic article
• Nilsen, Halvor Møll; Syversveen, Anne Randi; Lie, Knut-Andreas; Tveranger, Jan; Nordbotten, Jan Martin. (2012) Impact of top-surface morphology on CO2 storage capacity. International Journal of Greenhouse Gas Control
  Academic article
• Lie, Knut-Andreas; Natvig, Jostein Roald; Nilsen, Halvor Møll. (2012) Discussion of dynamics and operator splitting techniques for two-phase flow with gravity. International Journal of Numerical Analysis & Modeling
  Academic article
• Nilsen, Halvor Møll; Natvig, Jostein Roald; Lie, Knut-Andreas. (2012) Accurate Modeling of Faults by Multipoint, Mimetic, and Mixed Methods. SPE Journal
  Academic article
• Lie, Knut-Andreas; Krogstad, Stein; Ligaard, Ingeborg S; Natvig, Jostein Roald; Nilsen, Halvor Møll; Skaflestad, Bård. (2012) Open-source MATLAB implementation of consistent discretisations on complex grids. Computational Geosciences
  Academic article
• Syversveen, Anne Randi; Nilsen, Halvor Møll; Lie, Knut-Andreas; Tveranger, Jan; Abrahamsen, Petter. (2012) A Study on How Top-Surface Morphology Influences the Storage Capacity of CO2 in Saline Aquifers.
  Academic chapter/article/Conference paper
• Hauge, Vera Louise; Lie, Knut-Andreas; Natvig, Jostein Roald. (2012) Flow-based coarsening for multiscale simulation of transport in porous media. Computational Geosciences
  Academic article
• Nilsen, Halvor Møll; Lie, Knut Andreas; Natvig, Jostein Roald. (2012) Accurate modelling of faults by multipoint, mimetic, and mixed methods. SPE Journal
  Academic article

2011

• Krotkiewski, Marcin; Ligaard, Ingeborg S; Lie, Knut-Andreas; Schmid, Daniel Walter. (2011) On the importance of the Stokes-Brinkman equations for computing effective permeability in karst reservoirs. Communications in Computational Physics
  Academic article
• Nilsen, Halvor Møll; Herrera, Paulo; Ashraf, Seyed Meisam; Ligaard, Ingeborg S; Iding, Martin; Hermanrud, Christian. (2011) Field-case simulation of CO2-plume migration using vertical-equilibrium models. Energy Procedia
  Academic article
• Natvig, Jostein Roald; Skaflestad, Bård; Bratvedt, Frode; Bratvedt, Kyrre; Lie, Knut-Andreas; Laptev, Vsevolod. (2011) Multiscale Mimetic Solvers for Efficient Streamline Simulation of Fractured Reservoirs. SPE Journal
  Academic article
• Alpak, Faruk Omer; Pal, Mayur; Lie, Knut-Andreas. (2011) A Multiscale Method for Modeling Flow in Stratigraphically Complex Reservoirs.
  Academic chapter/article/Conference paper

2010

• Ashraf, Seyed Meisam; Lie, Knut Andreas; Nilsen, Halvor Møll; Skorstad, Arne; Nordbotten, Jan M.. (2010) Impact of geological heterogeneity on early-stage CO2 plume migration.
  Academic chapter/article/Conference paper
• Gulbransen, Astrid Fossum; Hauge, Vera Louise; Lie, Knut-Andreas. (2010) A multiscale mixed finite-element method for vuggy and naturally-fractured reservoirs. SPE Journal
  Academic article
• Lie, Knut-Andreas. (2010) Multiscale methods for subsurface flow.
  Popular scientific chapter/article
• Brodtkorb, Bernt Andre; Hagen, Trond Runar; Lie, Knut-Andreas; Natvig, Jostein Roald. (2010) Simulation and visualization of the Saint-Venant system using GPUs. Computing and Visualization in Science
  Academic article
• Holden, Helge; Karlsen, Kenneth Hvistendahl; Lie, Knut-Andreas; Risebro, Nils Henrik. (2010) Splitting Methods for Partial Differential Equations with Rough Solutions. Analysis and Matlab Programs. European Mathematical Society (EMS) Press European Mathematical Society (EMS) Press
  Academic monograph
• Tjåland, Egil; Kvamsdal, Trond; Amundsen, Jørn Aslak; Lie, Knut-Andreas; Maincon, Philippe; Rønquist, Einar. (2010) Computational Science and Engineering: Challenges and Opportunities. NTNU og SINTEF NTNU og SINTEF
  Report

2009

• Tai, Xue-C.; Mørken, K.; Lysaker, O.M.; Lie, Knut-A.. (2009) Scale Space and Variational Methods in Computer Vision. Second International Conference, SSVM 2009. Springer Springer
  Academic anthology/Conference proceedings
• Eikemo, Birgitte; Lie, Knut-Andreas; Eigestad, Geir Terje; Dahle, Helge Ketil. (2009) Discontinuous Galerkin methods for advective transport in single-continuum models of fractured media. Advances in Water Resources
  Academic article
• Aarnes, JE; Lie, Knut-Andreas; Kippe, V; Krogstad, Stein. (2009) Multiscale methods for subsurface flow.
  Academic chapter/article/Conference paper
• Stenerud, Vegard Røine; Lie, KA; Kippe, V. (2009) Generalized travel-time inversion on unstructured grids. Journal of Petroleum Science and Engineering
  Academic article
• Gulbransen, Astrid Fossum; Hauge, Vera Louise; Lie, Knut-Andreas. (2009) A Multiscale Mixed Finite-Element Method for Vuggy and Naturally-Fractured Reservoirs.
  Academic chapter/article/Conference paper
• Nilsen, Halvor Møll; Lie, Knut-Andreas. (2009) Front-tracking methods for use in streamline simulation of compressible flow.
  Academic chapter/article/Conference paper
• Tai, Xue-Cheng; Mørken, Knut Martin; Lysaker, Marius; Lie, Knut-Andreas. (2009) Scale Space and Variational Methods in Computer Vision. Springer Springer
  Academic anthology/Conference proceedings

2008

• Stenerud, Vegard Røine; Kippe, Vegard; Lie, Knut-Andreas; Datta-Gupta, Akhil. (2008) Adaptive multiscale streamline simulation and inversion for high-resolution geomodels. SPE Journal
  Academic article
• Aarnes, Jørg Espen; Lie, Knut-Andreas; Kippe, Vegard; Krogstad, Stein. (2008) Multiscale methods for subsurface flow.
  Academic chapter/article/Conference paper
• Gulbransen, Astrid Fossum; Hauge, Vera Louise; Lie, Knut-Andreas. (2008) A multiscale mixed finite-element method for vuggy and naturally-fractured reservoirs.
  Academic chapter/article/Conference paper
• Nilsen, Halvor Møll; Lie, Knut-Andreas. (2008) On Front Tracking for Compressible Flow.
  Academic chapter/article/Conference paper
• Natvig, Jostein Roald; Lie, Knut-Andreas. (2008) On Efficient Implicit Upwind Schemes.
  Academic chapter/article/Conference paper
• Kippe, Vegard; Aarnes, Jørg E.; Lie, Knut-Andreas. (2008) A comparison of multiscale methods for elliptic problems in porous media flow. Computational Geosciences
  Academic article
• Stenerud, Vegard Røine; Kippe, Vegard; Lie, Knut-Andreas; Datta-Gupta, Akhil. (2008) Adaptive multiscale streamline simulation and inversion for high-resolution geomodels. SPE Journal
  Academic article
• Aarnes, Jørg E.; Krogstad, Stein; Lie, Knut-Andreas. (2008) Multiscale mixed/mimetic methods on corner-point grids. Computational Geosciences
  Academic article
• Juanes, Ruben; Lie, Knut-Andreas. (2008) Numerical modeling of multiphase first-contact miscible flows. Part 2. Front-tracking/streamline simulation. Transport in Porous Media
  Academic article
• Natvig, Jostein Roald; Lie, Knut-Andreas. (2008) Fast computation of multiphase flow in porous media by implicit discontinuous Galerkin schemes with optimal ordering of elements. Journal of Computational Physics
  Academic article

2007

• Hægland, Håkon; Dahle, Helge K.; Eigestad, G. T.; Lie, Knut-Andreas; Aavatsmark, Ivar. (2007) Improved streamlines and time-of-flight for streamline simulation on irregular grids. Advances in Water Resources
  Academic article
• Juanes, Ruben; Lie, Knut-Andreas. (2007) Numerical modeling of multiphase first-contact miscible flows. Part 1. Analytical Riemann solver. Transport in Porous Media
  Academic article
• Hægland, Håkon; Dahle, Helge Ketil; Eigestad, Geir Terje; Lie, Knut-Andreas; Aavatsmark, Ivar. (2007) Improved streamlines and time-of-flight for streamline simulation on irregular grids. Advances in Water Resources
  Academic article
• Hagen, Trond Runar; Henriksen, Martin O.; Hjelmervik, Jon M.; Lie, Knut-Andreas. (2007) How to Solve Systems of Conservation Laws Numerically Using the Graphics Processor as a High-Performance Computational Engine.
  Encyclopedia article
• Hasle, Geir; Lie, Knut-Andreas; Quak, Ewald Gunther. (2007) Geometric Modelling, Numerical Simulation, and Optimization: Applied Mathematics at SINTEF. Springer Publishing Company Springer Publishing Company
  Academic anthology/Conference proceedings
• Stenerud, Vegard Røine; Lie, Knut-Andreas. (2007) Streamline-Based History Matching: A Review. SINTEF Digital SINTEF Digital
  Report
• Natvig, Jostein R.; Lie, Knut-Andreas; Eikemo, Birgitte; Berre, Inga. (2007) An efficient discontinuous Galerkin method for advective transport in porous media. Advances in Water Resources
  Academic article
• Tai, Xue-Cheng; Lie, Knut-Andreas; Chan, Tony F.; Osher, Stanley. (2007) Image Processing based on Partial differential equations. Springer Springer
  Academic anthology/Conference proceedings
• Hagen, Trond Runar; Henriksen, Martin O; Hjelmervik, Jon M.; Lie, Knut-Andreas. (2007) How to solve systems of conservation laws numerically using the graphics processor as a high-performance computational engine.
  Academic chapter/article/Conference paper
• Aarnes, Jørg E.; Kippe, Vegard; Lie, Knut-Andreas; Rustad, Alf Birger. (2007) Modelling of Multiscale Structures in Flow Simulations for Petroleum Reservoirs.
  Academic chapter/article/Conference paper
• Aarnes, Jørg E.; Gimse, Tore; Lie, Knut-Andreas. (2007) An Introduction to the Numerics of Flow in Porous Media using Matlab.
  Academic chapter/article/Conference paper
• Hasle, Geir; Lie, Knut-Andreas; Quak, Ewald Gunther. (2007) Geometric Modelling, Numerical Simulation, and Optimization: Applied Mathematics at SINTEF. Springer Springer
  Academic anthology/Conference proceedings

2006

• Hagen, Trond Runar; Lie, Knut-Andreas; Natvig, Jostein Roald. (2006) Solving the Euler equations on graphics processing units. Lecture Notes in Computer Science (LNCS)
  Academic article
• Hagen, Trond Runar; Lie, Knut-Andreas; Natvig, Jostein Roald. (2006) Solving the Euler Equations on Graphics Processing Units.
  Academic chapter/article/Conference paper
• Aarnes, Jørg; Krogstad, Stein; Lie, Knut-Andreas; Natvig, Jostein Roald. (2006) Fast sequential implicit porous media flow simulations using multiscale finite elements and reordering of cells for solution of nonlinear transport equation.
  Academic chapter/article/Conference paper
• Aarnes, Jørg; Kippe, V; Lie, Knut-Andreas. (2006) Multiscale methods and streamline simulation for rapid reservoir performance prediction.
  Academic chapter/article/Conference paper
• Aarnes, Jørg; Krogstad, Stein; Lie, Knut-Andreas; Laptev, V. (2006) Multiscale Mixed Methods on Corner-Point grids: Mimetic versus Mixed Subgrid Solvers. SINTEF Digital SINTEF Digital
  Report
• Tai, Xue-Cheng; Lie, Knut-Andreas; Chan, Tony; Osher, Stanley. (2006) Image Processing based on Partial differential equations. Springer Springer
  Academic anthology/Conference proceedings
• Aarnes, Jørg; Krogstad, Stein; Lie, Knut-Andreas. (2006) A hierarchical multiscale method for two-phase flow based upon mixed finite elements and nonuniform coarse grids. Multiscale Modeling & simulation
  Academic article

2005

• Berre, Inga; Karlsen, Kenneth Hvistendahl; Lie, Knut-Andreas; Natvig, Jostein R.. (2005) Fast computation of arrival times in heterogeneous media. Computational Geosciences
  Academic article
• Lie, Knut-Andreas; Aarnes, Jørg Espen; Kippe, Vegard; Krogstad, Stein. (2005) Multiscale Methods for Flow in Porous Media. Rakenteiden Mekaniikka
  Academic article
• Hagen, Trond R; Hjelmervik, Jon M.; Lie, Knut-Andreas; Natvig, Jostein Roald; Henriksen, M.. (2005) Visual simulation of shallow-water waves. Simulation modelling practice and theory
  Academic article
• Aarnes, Jørg Espen; Kippe, Vegard; Lie, Knut-Andreas. (2005) Mixed multiscale finite elements and streamline methods for reservoir simulation of large geomodels. Advances in Water Resources
  Academic article
• Berre, Inga; Dahle, Helge Ketil; Mannseth, Trond; Lie, Knut-Andreas. (2005) Fast Simulation of Transport and Adaptive Permeability Estimation in Porous Media. Universitetet i Bergen Universitetet i Bergen
  Doctoral dissertation
• Lie, Knut-Andreas; Juanes, Ruben. (2005) A front-tracking method for the simulation of three-phase flow in porous media. Computational Geosciences
  Academic article

2004

• Lie, K. A.; Tveito, Aslak. (2004) Development of a staggered central difference scheme that does not use a spatial reconstruction. Simula Research Laboratory Simula Research Laboratory
  Report

2003

• Berre, I.; Karlsen, Kenneth Hvistendahl; Lie, Knut-Andreas; Natvig, Jostein Roald. (2003) Fast computation of arrival times in heterogeneous. Universitetet i Oslo Universitetet i Oslo
  Report
• Lie, Knut-Andreas. (2003) On the artificial compression method for second-order nonoscillatory central difference schemes for systems of conservation laws. SIAM Journal on Scientific Computing
  Academic article
• Lie, Knut-Andreas. (2003) An improved quadrature rule for the flux-computation in staggered central difference schemes in multidimensions. Journal of Scientific Computing
  Academic article

2002

• Berre, Inga; Dahle, Helge Ketil; Karlsen, Kenneth H.; Lie, Knut-Andreas; Natvig, Jostein R.. (2002) Time-of-flight + fast Marching + transport collapse: an alternative to streamlines for tow-phase porous media flow with capillary forces?. Developments in Water Science
  Academic article

2001

• Haugse, Vidar; Karlsen, Kenneth Hvistendahl; Lie, Knut-Andreas; Natvig, Jostein. (2001) Numerical solution of the polymer system by front tracking. Transport in Porous Media
  Academic article
• Karlsen, Kenneth Hvistendahl; Lie, Knut-Andreas; Natvig, Jostein Roald; Nordhaug, Hans Fredrik; Dahle, Helge Ketil. (2001) Operator splitting methods for systems of convection-diffusion equations: nonlinear error mechanisms and correction strategies. Journal of Computational Physics
  Academic article
• Haugse, Vidar; Karlsen, Kenneth Hvistendahl; Lie, Knut-Andreas; Natvig, Jostein Roald. (2001) Numerical solution of the polymer system by front tracking. Transport in Porous Media
  Academic article
• Dahle, Helge Ketil; Karlsen, Kenneth Hvistendahl; Lie, Knut-A.; Natvig, Jostein R.. (2001) Corrected operator splitting for systems of convection-diffusion equations. MANGLER
  Academic article

2000

• Holden, Helge; Karlsen, Kenneth Hvistendahl; Lie, Knut-Andreas. (2000) Operator splitting methods for degenerate convection-diffusion equations I: convergence and entropy estimates. CMS Conference Proceedings Series
  Academic article
• Karlsen, Kenneth Hvistendahl; Lie, Knut-Andreas; Risebro, Nils Henrik. (2000) A fast marching method for reservoir simulation. Computational Geosciences
  Academic article
• Lie, Knut-Andreas. (2000) Front tracking for one-dimensional quasilinear hyperbolic equations with variable coefficients. Numerical Algorithms
  Academic article
• Bürger, Raymond; Evje, Steinar; Karlsen, Kenneth Hvistendahl; Lie, Knut-Andreas. (2000) Numerical methods for the simulation of the settling of flocculated suspensions. Chemical Engineering Journal
  Academic article
• Evje, Steinar; Karlsen, Kenneth Hvistendahl; Lie, Knut-Andreas; Risebro, Nils Henrik. (2000) Front tracking and operator splitting for nonlinear degenerate convection-diffusion equations. IMA Journal of Applied Mathematics
  Academic article
• Holden, Helge; Karlsen, Kenneth Hvistendahl; Lie, Knut-Andreas. (2000) Operator splitting methods for degenerate convection-diffusion equations II: numerical examples with emphasis on reservoir simulation and sedimentation. Computational Geosciences
  Academic article

1999

• Karlsen, Kenneth Hvistendahl; Lie, K-A; Risebro, NH. (1999) A fast level set method for reservoir simulation. Universitetet i Bergen Universitetet i Bergen
  Report
• Haugse, V; Karlsen, Kenneth Hvistendahl; Lie, K-A; Natvig, JR. (1999) Numerical solution of the polymer system by front tracking. Universitetet i Bergen Universitetet i Bergen
  Report
• Holden, Helge; Lie, Knut-Andreas; Risebro, Nils Henrik. (1999) An unconditionally stable method for the Euler equations. Journal of Computational Physics
  Academic article
• Holdahl, Runar; Holden, Helge; Lie, Knut-Andreas. (1999) Unconditionally stable splitting methods for the shallow water equations. BIT Numerical Mathematics
  Academic article
• Karlsen, Kenneth Hvistendahl; Lie, Knut-Andreas. (1999) An unconditionally stable splitting scheme for a class of nonlinear parabolic equations. IMA Journal of Numerical Analysis
  Academic article
• Lie, Knut-Andreas. (1999) A dimensional splitting method for quasilinear hyperbolic equations with variable coefficients. BIT Numerical Mathematics
  Academic article
• Karlsen, Kenneth Hvistendahl; Lie, Knut-Andreas. (1999) An unconditionally stable splitting for a class of nonlinear parabolicequations. IMA Journal of Numerical Analysis
  Academic article
• Holden, Helge; Karlsen, Kenneth Hvistendahl; Lie, K-A. (1999) Operator splitting methods for degenerate convection-diffusion equations II: numerical examples with emphasis on reservoir simulation and sedimentation. Universitetet i Bergen Universitetet i Bergen
  Report
• Holden, Helge; Karlsen, Kenneth Hvistendahl; Lie, K-A. (1999) Operator splitting methods for degenerate convection-diffusion equations I: convergence and entropy estimates. Universitetet i Bergen Universitetet i Bergen
  Report
• Holdahl, Runar; Holden, Helge; Lie, Knut Andreas. (1999) Unconditionally stable splitting methods for the shallow water equations. BIT Numerical Mathematics
  Academic article
• Holden, Helge; Lie, Knut-Andreas; Risebro, N.H.. (1999) An Unconditionally Stable Method for the Euler Equations. Journal of Computational Physics
  Academic article

1998

• Karlsen, Kenneth Hvistendahl; Lie, Knut-Andreas; Risebro, Nils Henrik; Frøyen, Johnny. (1998) A front-tracking approach to a two-phase fluid-flow model with capillary forces. In situ
  Academic article
• Karlsen, Kenneth Hvistendahl; Brusdal, Kari; Dahle, Helge Ketil; Evje, S.; Lie, K-A. (1998) The corrected operator splitting approach applied to a nonlinear advection-diffusion problem. Computer Methods in Applied Mechanics and Engineering
  Academic article
• Karlsen, Kenneth Hvistendahl; Lie, Knut-Andreas; Risebro, Nils Henrik; Frøyen, Johnny. (1998) A front-tracking approach to a two-phase fluid-flow model with capillary forces. In situ
  Academic article

1997

• Karlsen, Kenneth Hvistendahl; Brusdal, Kari; Dahle, Helge Ketil; Evje, Steinar; Lie, Knut-Andreas. (1997) The corrected operator splitting approach to a nonlinear advection-diffusion problem. Applied Mathematics Report
  Academic article