Numerical Methods for Partial Differential Equations

Finite element methods for the discretization of (multidimensional) elliptic boundary value problems: a priori and a posteriori error analysis, adaptive mesh refinement, fast solvers. Introduction to numerical methods for evolution equations

After successful completion of the module the students are able to understand and apply numerical solution techniques for partial differential equations. They have programming skills and are able to handle corresponding software.

MA0008 Numerical Analysis, MA3301 Numerics of Differential Equations

lecture, exercise course, self-study assignments
The module is offered as lectures with accompanying practice sessions. In the lectures, the contents will be presented in a talk with demonstrative examples, as well as through discussion with the students. The lectures should animate the students to carry out their own analysis of the themes presented and to independently study the relevant literature. Corresponding to each lecture, practice sessions will be offered, in which exercise sheets and solutions will be available. In this way, students can deepen their understanding of the methods and concepts taught in the lectures and independently check their progress. At the beginning of the module, the practice sessions will be offered under guidance, but during the term the sessions will become more independent, and intensify learning individually as well as in small groups.

blackboard

Iserles, A.: A first course in the numerical analysis of differential equations. Cambridge University Press, Cambridge, 1996.
Morton, K. W.; Mayers, D. F.: Numerical solution of partial differential equations. An introduction. Second edition. Cambridge University Press, Cambridge, 2005.

The module examination is based on a written exam (90 minutes). Students have to know basic methods to deal with partial differential equations and can apply them in limited time. They show their programming skills in the corresponding software.