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Rapid error reduction for block Gauss–Seidel based on p ‐hierarchical basis
Author(s) -
Le Borne S.,
Ovall J.S.
Publication year - 2013
Publication title -
numerical linear algebra with applications
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.02
H-Index - 53
eISSN - 1099-1506
pISSN - 1070-5325
DOI - 10.1002/nla.1841
Subject(s) - mathematics , gauss–seidel method , block (permutation group theory) , reduction (mathematics) , basis (linear algebra) , algorithm , iterative method , combinatorics , geometry
SUMMARY 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 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 on uniform and adapted meshes support these claims. Copyright © 2012 John Wiley & Sons, Ltd.