Differential Equations and Numerical Analysis (DNA)
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
Seminars and 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 nonlocal 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, wavebreaking, or peaks and cusps at the surface.
 Norwegian Research Centre for Offshore Wind Technology (NOWITECH) (20092017)
 Centre for Environmentalfriendly Energy Research. Cofunded by NFR and industrial partners.
Courses taught by the DNA Group
Bachelor and Master Level
 TMA4165 Differential Equations and Dynamical Systems
 TMA4180 Optimization I
 TMA4183 Optimization II
 TMA4195 Mathematical modelling
 TMA4205 Numerical Linear Algebra
 TMA4212 Numerical Solution of Differential Equations by Difference Methods
 TMA4215 Numerical Mathematics
 TMA4220 Numerical Solution of Partial Differential Equations Using Element Methods
 TMA4305 Partial Differential Equations
 TMA4320 Introduction to Scientific Computation
PhD Level
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 microsized sensors under the influence of electrolyte flow
Journal of Electroanalytical Chemistry
Odd Andersen, KnutAndreas Lie and Halvor Møll Nilsen
An OpenSource Toolchain for Simulation and Optimization of AquiferWide CO2 Storage
Energy Procedia
Elena Celledoni, Bawfeh Kingsley Kometa and Olivier Verdier
High order semiLagrangian methods for the incompressible NavierStokes equations
Journal of Scientific Computing
Peter Lindqvist and Juan Manfredi
On the mean value property for the pLaplace 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