Uniform convergence of the multigrid V-cycle for an anisotropic problem (Q2701544)
From MaRDI portal
 | This is the item page for this Wikibase entity, intended for internal use and editing purposes. Please use this page instead for the normal view: Uniform convergence of the multigrid V-cycle for an anisotropic problem |
scientific article
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Uniform convergence of the multigrid V-cycle for an anisotropic problem |
scientific article |
Statements
19 February 2001
0 references
uniform convergence
0 references
Galerkin method
0 references
error bounds
0 references
finite element
0 references
anisotropic problems
0 references
V-cycle multigrid method
0 references
0 references
0 references
0 references
0 references
0 references
Uniform convergence of the multigrid V-cycle for an anisotropic problem (English)
0 references
The linear systems arising from the standard finite element discretizations of certain second-order anisotropic problems with variable coefficients on a rectangle are considered. The performance of a V-cycle multigrid method applied to the finite element equations is studied and a modification of the theory of \textit{D. Braess} and \textit{W. Hackbusch} [SIAM J. Numer. Anal. 20, 967-975 (1983; Zbl 0521.65079)] is presented.NEWLINENEWLINENEWLINEIt is shown that the V-cycle multigrid iteration with a line smoother is a uniform contraction in the energy norm. In the verification of the hypotheses in this theory, a weighted \(L^2\)-norm estimate for the error in the Galerkin finite element approximation and a smoothing property of the line smoothers is applied and proved in this paper.
0 references
