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

Espen R. JakobsenProfessor Espen R. Jakobsen
Head of the DNA Group

 

Staff – DNA Group

Recent Publications

Seminars and Conferences

Seminars

Conferences

Current Projects

Challenges in Preservation of Structure (CHiPS)

Challenges in Preservation of Structure is a EU Horizon 2020 project that will address challenges in preservation of structure for the numerical solution of evolutionary problems. The scientific innovations of the project will be incorporated into usable software tools in cooperation with our non-academic partner MathWorks.

Waves and Nonlinear Phenomena (WaNP)

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

Funded by FRIPRO Toppforsk, 2016–2020.

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

The main purpose of Structure Preserving Integrators, Discrete Integrable Systems and Algebraic Combinatorics 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. The SPIRIT project runs from 2014 to 2017.

Nonlinear Water Waves

Nonlinear water waves 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.

The project runs from 2014 to 2017.

Norwegian Research Centre for Offshore Wind Technology (NOWITECH)

Norwegian Research Centre for Offshore Wind Technology is sponsored by Centre for Environmental-friendly Energy Research, co-funded by NFR and industrial partners, and runs from 2009 to 2017.