Department of Mathematical Sciences

Differential Equations and Numerical Analysis (DNA)

Simulation of Kelvin-Helmholtz instability. Figure.

The DNA group works in the following areas:

Partial differential equations can be used to model phenomena such as gas flow through a pipeline or in porous media, water waves over an ocean or stock prices. Since Isaac Newton's initial studies, this field has witnessed an enormous development, and today practically all laws of nature are expressed in terms of differential equations. Central questions include whether there exists a solution of the equation; whether it is unique; and whether it is stable with respect to initial or boundary data.

Numerical methods of differential equations approximate the solution of a differential equation in a way suitable for implementation on computers. Thanks to advances in the field of numerical methods the past few decades, we have gotten better weather forecasts, safer cars and air planes, and we can predict the impact of tsunamis before they hit the shore.

Optimization theory covers problems where the main interest lies in finding the smallest or largest possible values of a function, given certain conditions. Such problems appear in a large number of physical models (such as minimal energy or entropy principles); medical or geophysical measurements (such as parameter identification or inverse problems); and improvements in the performance of technical or other systems (such as shape optimization).

We also teach a number of courses and offer project and master theses in the above areas.

Contact

Elena CelledoniProfessor Elena Celledoni, Head of the DNA group

 

Staff – DNA group

Seminars and Conferences

Seminars

Conferences

  • No upcoming conferences

Current Projects

Waves and Nonlinear Phenomena (WaNP) (FRIPRO Toppforsk, 2016–2020)

The main goal of WaNP is to analyze the interplay of singularities and nonlocal effects in the solutions of partial differential equations that model wave phenomena.

Structure Preserving Integrators, Discrete Integrable Systems and Algebraic Combinatorics (SPIRIT) (2014–2017)

The main purpose of this project is to develop and analyse specially tailored numerical methods for approximating the solution to differential equations.

The work is focused on numerical methods which retain selected qualitative properties of the exact solution.

Nonlinear water waves (2014–2017)
This project aims at studying certain classes of non-local equations which describe water waves in a canal or out at sea, with a particular focus on waves that allow for stagnation, like interior vortices, wave-breaking, or peaks and cusps at the surface.
Norwegian Research Centre for Offshore Wind Technology (NOWITECH) (2009-2017)
Centre for Environmental-friendly Energy Research. Co-funded by NFR and industrial partners.

Completed projects

Recent Publications

Bolaji James Adesokan, X. Quan, Anton Evgrafov, Arto Heiskanen, Anja Boisen and Mads Peter Sørensen
Experimentation and numerical modeling of cyclic voltammetry for electrochemical micro-sized sensors under the influence of electrolyte flow
Journal of Electroanalytical Chemistry

Odd Andersen, Knut-Andreas Lie and Halvor Møll Nilsen
An Open-Source Toolchain for Simulation and Optimization of Aquifer-Wide CO2 Storage
Energy Procedia

Elena Celledoni, Bawfeh Kingsley Kometa and Olivier Verdier
High order semi-Lagrangian methods for the incompressible Navier-Stokes equations
Journal of Scientific Computing

Peter Lindqvist and Juan Manfredi
On the mean value property for the p-Laplace equation in the plane
Proceedings of the American Mathematical Society

Peter Lindqvist and Juha Kinnunen
Unbounded supersolutions of some quasilinear parabolic equations: A dichotomy
Nonlinear Analysis

Annette Stahl and Trond Kvamsdal
New Visualization Techniques for Isogeometric Analysis Results
Computer Methods in Applied Mechanics and Engineering

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