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MiS Preprint

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

Sabine Le Borne and Jeffrey Ovall


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.

MSC Codes:
65N22, 65N55, 65N30, 65F08, 65F05
higher-order finite elements, hierarchical bases, hierarchical matrices, block Gauss-Seidel

Related publications

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