Numerical Solution of Initial Boundary Value Problems, 3.0 credits

Entry requirements

Good general knowledge in: calculus, integrals, differentiation, fouriertransforms, linear algebra, functional analysis, programming.

Contents

1. General principles and ideas. Periodic solutions and Fourier analysis. The Petrovski condition for the PDE and the von Neumann condition for difference schemes.

2. The energy method. Semi-bounded operators. Symmetric and skewsymmetric operators. Well-posed boundary conditions in practise. The error equation. Energy estimates. Accuracy of discrete approximation.

3. High order finite difference methods. Boundary treatment. Summation by parts (SBP) operators. Weak boundary conditions. Strict/time stability.

4. Extension to multiple dimensions. Structured multi-block methods. Unstructured finite volume methods and discontinuous Galerkin methods. Stability and conservation.

Educational methods

6 Lectures, 3 excersises, 3 seminars. Approximately 20 hours.

Examination

3 mandatory HWs.

Grading

Course literature

Lecture notes and reference to relevant articles.