Rapid error reduction for block Gauss-Seidel based on p-hierarchical bases
Sabine Le Borne and Jeffrey Ovall
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Submission date: 06. Jun. 2011 (revised version: June 2011)
MSC-Numbers: 65N22, 65N55, 65N30, 65F08, 65F05
Keywords and phrases: higher-order finite elements, hierarchical bases, hierarchical matrices, block Gauss-Seidel
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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 H1-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.