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 mesh 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 equation systems, 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 of either C++ or MATLAB programming. (At least you should be willing to learn during the course.) If you prefer to program in another language that 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 developed 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, or Applied Mathematics: Body and Soul by Eriksson, Estep, and Johnson.

Consultation

I prefer to answer questions by email. If you need to meet me for a discussion, I will be available at my office between 9-12 each Wednesday.

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.

Puffin

Alternatively, you can use Puffin, which is a minimal version of DOLFIN for Matlab/Octave.