Schwarz Methods for Partial Differential Equations


Domain Decomposition Methods for Partial Differential Equations have become topics of intense interest in research over the past years because they not only provide effective computing strategies suitable for high performance computing but can provide an elegant and complete analysis of the algorithms. In these lectures, I will focus on the mathematical foundation of domain decomposition concentrating our effort on a study of lower order finite element approximation of Poisson's equation. The goal is to provide the basics of the theory in order to demonstrate what mathematical tools are required and what can be done. The topics that I plan to cover:

If time permits: