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Rapid error reduction for block Gauss-Seidel based on p-hierarchical basis
Publikationstyp
Journal Article
Date Issued
2012-05-08
Sprache
English
Author(s)
Institut
TORE-URI
Volume
20
Issue
5
Start Page
743
End Page
760
Citation
Numerical Linear Algebra with Applications 5 (20): 743-760 (2013)
Publisher DOI
Publisher
Wiley
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.
Subjects
block gauss-seidel
hierarchical bases
hierarchical matrices
higher-order finite elements
DDC Class
510: Mathematik