On the Robustness of Two-level Methods for FEM Anisotropic Elliptic Problems

Maria Lymbery

March 29, 2011, 3:30 p.m. HS 14

We study the construction of robust two-level methods for elliptic boun-
dary value problems where the focus is on mesh and coecient anisotropy.
It is known that the standard hierarchical basis (HB) transformation does
not result in a splitting in which the angle between the coarse space and its
(hierarchical) complement is uniformly bounded with respect to the ratio of
anisotropy when quadratic elements are used in the process of discretization.
In this talk, however, we present some rst results on a robust splitting of
the nite element space of continuous piecewise quadratic functions for the
orthotropic elliptic problem. Moreover, we comment on a speci c technique of
sparse Schur complement approximation and present a numerical comparison
between the two approaches.
This is a joint work with Johannes Kraus (RICAM, Austria) and Svetozar
Margenov (IICT, Bulgaria).