DMCA
Schwarz Preconditioners for Elliptic Problems with Discontinuous Coefficients Using Conforming and Non-Conforming Elements (1994)
| Citations: | 1 - 0 self |
BibTeX
@MISC{Martins94schwarzpreconditioners,
author = {Marcus V. Sarkis Martins},
title = {Schwarz Preconditioners for Elliptic Problems with Discontinuous Coefficients Using Conforming and Non-Conforming Elements},
year = {1994}
}
Share
 |
 |
 |
 |
||
OpenURL
Abstract
Additive multilevel Schwarz methods are developed for conforming finite element approximations of second order elliptic problems. We focus on problems in three dimensions with possibly large jumps in the coefficients across the interface separating the subregions. We establish condition number estimates for the iterative operators, which are independent of the coefficients, and grow at most as the square of the number of levels `. For the multiplicative versions, such as the V-cycle multigrid methods using Gauss Seidel and damped Jacobi smoothers, we obtain a rate of convergence bounded from above by 1 \Gamma C ` \Gamma2 . We also characterize a class of distributions of values of the coefficients, called quasi-monotone, for which the error of the weighted L 2 -projection is stable and for which we can use the standard piecewise linear functions as a coarse space and obtain condition number estimates independent of the number of levels, subregions, and the coefficients. We also des...
Keyphrases
non-conforming element discontinuous coefficient elliptic problem schwarz preconditioners coarse space iterative operator multiplicative version additive multilevel schwarz method finite element approximation large jump second order elliptic problem condition number estimate v-cycle multigrid method standard piecewise linear function jacobi smoother condition number gauss seidel
