Article
Rapid error reduction for block Gauss–Seidel based on p-hierarchical basis
Numerical Linear Algebra with Applications
(2013)
Abstract
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.
Disciplines
Publication Date
2013
DOI
10.1002/nla.1841
Citation Information
Jeffrey S. Ovall. "Rapid error reduction for block Gauss–Seidel based on p-hierarchical basis" Numerical Linear Algebra with Applications (2013) Available at: http://works.bepress.com/jeffrey_ovall/44/