Author: Joseph E. Pasciak
Title of the contribution: Multigrid and domain decomposition preconditioners for the Hellinger-Reissner formulation of linear ellasticity
Abstract:
In this talk, we develop a multigrid preconditioner for the discrete system of linear equations that results from the mixed formulation of the linear plane elasticity problem using the Arnold-Winther elements.
This, in turn, can be reduced to the problem of finding a multigrid preconditioner for the form (u,v)+(div u, div v) in the symmetric matrix space resulting from Arnold-Winther elements.
Since the form is not uniformly elliptic, a Helmholtz-type decomposition is essential.
The Arnold-Winther finite element space gives rise to non-nested multilevel spaces adding difficulty to the analysis.
We give results showing that overlapping domain decomposition techniques and a the variable V-cycle multigrid algorithm lead to an optimal preconditioner.
URL: www.ricam.oeaw.ac.at/specsem/sscm/srs_ev/difcome/program/abstracts/abstract_pasciak.php
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