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.