Numerical Solution of Initial Boundary Value Problems/
Numerisk lösning av initial och randvärdesproblem
Number of credits: 3 hp
Examiner: Jan Nordström
Course literature: Lecture notes and reference to relevant articles.
Course 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.
Organisation: 6 Lectures, 3 excersises, 3 seminars. Approximately 20 hours.
Examination: 3 mandatory HWs.
Prerequisites: Good general knowledge in: calculus, integrals, differentiation, fouriertransforms, linear algebra, functional analysis, programming.
Last updated: 2017-10-16