===affil2:
TU München
===firstname:
Ulrich
===firstname4:
Herbert
===firstname3:
Barbara
===lastname2:
Waluga
===lastname:
Ruede
===firstname5:

===affil6:

===lastname3:
Wohlmuth
===email:
ruede@cs.fau.de
===lastname6:

===affil5:

===otherauths:

===lastname4:
Egger
===affil4:
TU Darmstadt
===lastname7:

===affil7:

===firstname7:

===postal:
Universitaet Erlangen
Cauerstrasse 11
91080 Erlangen
Germany
===firstname6:

===ABSTRACT:
Elliptic problems with reentrant corners exhibit the well-known pollution-effect, i.e. the convergence deteriorates in global norms. This can be avoided by many techniques, such as a suitable mesh grading or by enriching the finite element spaces. Here we analyze a new method that restores optimal converge in weighted norms and that differs form alternatives in requiring only local corrections on uniform or quasi-uniform grids. We show that the corrections must be such that the modified finite element discretization reproduces the energy of the solution with sufficient accuracy. This can be achieved by a suitable modification in a small, fixed number of elements. The corresponding stiffness matrix differs from the uncorrected one in only a few numerical values. The correction parameter for each reentrant corner can be computed efficiently in a multi-scale approach that can be  integrated in a full multigrid method. 

===affil3:
TU München
===lastname5:

===affilother:

===title:
A multi-scale algorithm to recover optimal convergence in the presence of
corner singularities
===firstname2:
Christian