Title / Abstract
Boundary Integral Equations and the Boundary Element MethodThe lectures will provide a brief introduction to boundary integral equations and boundary element methods for scalar 2nd-order elliptic problems. Emphasis will be on formal derivations and algorithmic aspects.
- 2nd-order elliptic boundary value problems, Sobolev spaces, variational formulation and trace spaces
- fundamental solutions
- formal derivation of representation formulas
- boundary integral equations in variational form
- boundary element Galerkin discretization
Introduction Boundary Element Methods - Handout
Exercises
- R. Hiptmair, Exercise Project
References
- S.A. Sauter and Ch. Schwab, Boundary Element Methods. Springer Series in Computational Mathematics 39, Springer 2011: This is the main reference for the lecture, in particular Sections 3.1-3.5, 4.1-4.3, 5.1-5.3.
- G.C. Hsiao and W.L. Wendland, Boundary Integral Equations, Springer Series in Applied Mathematical Sciences 164, Springer 2008.
- O. Steinbach Numerical Approximation Methods for Elliptic Bondary Value Problems. Finite and Boundary Elements. Springer 2008. Relevant for the lecture are Chapters 5,6,7,10, and 12.
