Course description

Differential equations, ODEs or PDEs, can be solved by general methods, and in this course you will learn how to write a solver for your favourite differential equation. Or perhaps you are more interested in other related aspects of numerical solution of PDEs, such as grid generation, or iterative methods for linear systems?

Whatever your interest is, you are free to choose your own project and present your work at the end of the course in the form of a report and a short seminar. Suggestions for projects will be given, some more oriented towards programming, and some towards mathematical modeling.

At the beginning of the course, there will be a short series of lectures, giving a brief overview of some important issues related to numerical approximation of PDEs, including the finite element method, solution of large sparse systems of algebraic equations, error estimation and adaptivity, and issues related to computer implementation of such algorithms. We will also discuss C++ programming in Unix (or GNU/Linux) environments.

You are expected to have some knowledge in either C++ or MATLAB programming. (At least you should be willing to learn during the course.) If you prefer to program in another language this is also ok, but then you are more or less on your own. Hopefully, most of you will choose to do your projects within DOLFIN, which is an open-source platform for research and teaching in adaptive finite element methods at the Department of Computational Mathematics.

Literature

You are encouraged to find your own literature on your subject of interest, but a good starting point is Computational Differential Equations by Eriksson, Estep, Hansbo and Johnson.

Consultation

At some point, you will probably need some help with your projects. I prefer to answer questions by email, but if necessary we can schedule an appointment in my office.

DOLFIN

It is recommended (but not required!) that you do your projects within DOLFIN. Hopefully your projects will contribute to further improvement of the code.