# DK Nanocell Colloquium I

"Adaptive finite elements"

Many problems in applied sciences are described by means of partial differential

equations. Nowadays, the finite element method (FEM) belongs to the most efficient

methods for the computer simulation of such processes.

Usually the finite element mesh is uniformly refined which leads to huge discrete

problems. In adaptive finite element methods, a sequence of meshes is obtained from

the initial mesh by refining the mesh only in part in which the estimated error of the

solution is large.

This lecture gives an overview about finite elements. We start with some motivating

examples and investigate the ingredients of an adaptive algorithm

- error estimators and

- local refinement algorithms.

The presentation includes several numerical examples.