Martin Costabel (Rennes. France)

The h-p version of the weighted regularization method

Abstract

In the approximation of Maxwell boundary value problems on domains with reentrant corners by nodal finite elements, special attention has to be paid to the right choice of the variational formulation. It is known that a wrong choice can lead to unstable methods or to the approximation of non-physical objects. Using the weighted regularization method, one obtains a convergent finite element scheme. In its h-p version, it converges exponentially. For its analysis, one needs to consider $C^1$ interpolations.