Publisher DOI: 10.1002/nla.1841
Title: Rapid error reduction for block Gauss-Seidel based on p-hierarchical basis
Language: English
Authors: Le Borne, Sabine  
Ovall, Jeffrey S. 
Keywords: block gauss-seidel; hierarchical bases; hierarchical matrices; higher-order finite elements
Issue Date: 8-May-2012
Publisher: Wiley
Source: Numerical Linear Algebra with Applications 5 (20): 743-760 (2013)
Abstract (english): 
We consider a two-level block Gauss-Seidel iteration for solving systems arising from finite 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 the 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 on uniform and adapted meshes support these claims.
ISSN: 1099-1506
Journal: Numerical linear algebra with applications 
Institute: Mathematik E-10 
Document Type: Article
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