Two-Level Schwarz Methods for Nonconforming Finite Elements and Discontinuous Coefficients (1993)
| Venue: | Proceedings of the Sixth Copper Mountain Conference on Multigrid Methods, Volume 2, number 3224 |
| Citations: | 20 - 1 self |
BibTeX
@INPROCEEDINGS{Sarkis93two-levelschwarz,
author = {Marcus Sarkis},
title = {Two-Level Schwarz Methods for Nonconforming Finite Elements and Discontinuous Coefficients},
booktitle = {Proceedings of the Sixth Copper Mountain Conference on Multigrid Methods, Volume 2, number 3224},
year = {1993},
pages = {543--566},
publisher = {NASA}
}
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Abstract
. Two-level domain decomposition methods are developed for a simple nonconforming approximation of second order elliptic problems. A bound is established for the condition number of these iterative methods, which grows only logarithmically with the number of degrees of freedom in each subregion. This bound holds for two and three dimensions and is independent of jumps in the value of the coefficients. Key words. domain decomposition, elliptic problems, preconditioned conjugate gradients, nonconforming finite elements, Schwarz methods AMS(MOS) subject classifications. 65F10, 65N30, 65N55 1. Introduction. The purpose of this paper is to develop a domain decomposition methods for second order elliptic partial differential equations approximated by a simple nonconforming finite element method, the nonconforming P 1 elements. We consider a variant of a two-level additive Schwarz method introduced in 1987 by Dryja and Widlund [5] for a conforming case. In these methods, a preconditioner i...
