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

## Maria Lymbery

**March 29, 2011, 1:30 p.m. HS 14**

We study the construction of robust two-level methods for elliptic boundary value problems where the focus is on mesh and coeffcient 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 first results on a robust splitting of the finite element space of continuous piecewise quadratic functions for the orthotropic elliptic problem. Moreover, we comment on a specific 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).