Numerical Solution of Initial Boundary Value Problems – 2017
Number of credits: 3 hp
Linköping University, Department of Mathematics
16-20 October 2017, 5 full days.
Course literature: Lecture notes and reference to relevant articles.
More material in GUS: “High order difference methods for time-dependent PDE” by Gustafsson,B., Springer Series in Computational Mathematics (2008).
For theoretical details see also: GKO: “Time-dependent problems and difference methods” by Gustafsson, B., Kreiss, H.-O., and Oliger, J. John Wiley and Sons (1995).
- General principles and ideas. Periodic solutions and Fourier analysis. The Petrovski condition for the PDE and the von Neumann condition for difference schemes.
- The energy method. Semi-bounded operators. Symmetric and skew-symmetric operators. Well-posed boundary conditions. The error equation. Energy estimates. Accuracy of semi-discrete approximation.
- High order finite difference methods. Boundary treatment. Summation by parts (SBP) operators. Weak boundary conditions. Strict/time stability.
- Extension to multiple dimensions. Structured multi-block methods. Unstructured finite volume methods and discontinuous Galerkin methods. Stability and conservation.
- Time-integration and fully discrete stability.
Before the course: 1 week of study on material that I send out.
During the course: 5 Lectures, 3 excersises, 2 seminars. Approximately 15 hours.
After the course: 1 week of work with homework
Examination: 3 mandatory HWs.
Good general knowledge in: calculus, integrals, differentiation, Fourier-transforms, linear algebra, functional analysis, programming.