Multigrid methods are iterative solvers for large systems of linear
equations. The idea is not to use only one finite element mesh, but a
whole hierarchy of grids. The algorithm combines cheap iterative
methods on each level. The result is an equation solver of optimal
While the principle is very simple, a rigoros analysis is quite
envolved. It requires results from partial differential equations,
finite element analysis, Hilbert space theory as well as linear
algebra. The topics to the lecture is to discuss the analysis of mg.
In the first part, we consider various techniques for a simple
model problem. This chapter is split into no-regularity techniques
and techniques based on shift theorems.
The second part discusses extensions to non-standard problems as
non-conforming methods, mixed finite elements,
parameter dependent problemes,
An incremental script
(last update on May 16).