Weighted Poincaré inequalities and applications in domain decomposition

Dr. Clemens Pechstein

March 16, 2010, 3:30 p.m. HS 13

Poincaré type inequalities play a central role in the analysis of domain decomposition and multigrid methods for second-order elliptic problems. However, when the diffusion coefficient varies within a subdomain or within a coarse grid element, then standard condition number bounds for these methods may be overly pessimistic.

In this talk we present new weighted Poincaré type inequalities for a class of piecewise constant coefficients that lead to sharper bounds independent of any possible large contrasts in the coefficients. In particular we discuss overlapping Schwarz methods and finite element tearing and interconnecting
(FETI) methods. Numerical results are shown for FETI applied to a nonlinear magnetostatic field problem.

This talk is on joint work with Robert Scheichl, University of Bath (UK) and has been supported by the Austrian Science Founds (FWF) under grants P19255 and W1214.