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We have decided to discontinue the publication of preprints on our preprint server as of 1 March 2024. The publication culture within mathematics has changed so much due to the rise of repositories such as ArXiV (www.arxiv.org) that we are encouraging all institute members to make their preprints available there. An institute's repository in its previous form is, therefore, unnecessary. The preprints published to date will remain available here, but we will not add any new preprints here.

MiS Preprint
33/2011

Rapid error reduction for block Gauss-Seidel based on p-hierarchical bases

Sabine Le Borne and Jeffrey Ovall

Abstract

We consider a two-level block Gauss-Seidel iteration for solving systems arising from finite element element discretizations employing higher-order elements. A $p$-hierarchical basis is used to induce this block structure.

Using superconvergence results normally employed in the analysis of gradient recovery schemes, we argue that a massive reduction of $H^1$-error occurs in the first iterate, so that the discrete solution is adequately resolved in very few iterates---sometimes a single iteration is sufficient. Numerical experiments support these claims.

Received:
Jun 6, 2011
Published:
Jun 6, 2011
MSC Codes:
65N22, 65N55, 65N30, 65F08, 65F05
Keywords:
higher-order finite elements, hierarchical bases, hierarchical matrices, block Gauss-Seidel

Related publications

inJournal
2013 Repository Open Access
Sabine LeBorne and Jeffrey S. Ovall

Rapid error reduction for block GaussûSeidel based on p-hierarchical basis

In: Numerical linear algebra with applications, 20 (2013) 5, pp. 743-760