Stability of implicit extrapolation methods

U. Ruede
Institut fuer Informatik
Technische Universitaet Muenchen
Arcisstr. 21,
D-80290 Muenchen
Germany
ruede@informatik.tu-muenchen.de

Keywords: Implicit extrapolation, multigrid, multilevel subspace splitting
AMS Classification:     65N22, 65N50, 65N55}

Abstract

Multilevel methods are generally based on a splitting of the solution
space associated with a nested sequence of coarser grids.  Besides the
straightforward application of extrapolation on the grid system, we
propose to use extrapolation implicitly, similar to multigrid
tau-extrapolation.  This implicit extrapolation, when applied to linear
finite elements is related to the p-version of the finite element
method.  The method depends on a stability condition which must be
enforced by a suitable modification of the problem.