Two-level Additive Schwarz Preconditioners

for Nonconforming Finite Element Methods

Author:
Susanne C. Brenner

Journal:
Math. Comp. **65** (1996), 897-921

MSC (1991):
Primary 65F10, 65N30, 65N55

DOI:
https://doi.org/10.1090/S0025-5718-96-00746-6

MathSciNet review:
1348039

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Abstract | References | Similar Articles | Additional Information

Abstract: Two-level additive Schwarz preconditioners are developed for the nonconforming P1 finite element approximation of scalar second-order symmetric positive definite elliptic boundary value problems, the Morley finite element approximation of the biharmonic equation, and the divergence-free nonconforming P1 finite element approximation of the stationary Stokes equations. The condition numbers of the preconditioned systems are shown to be bounded independent of mesh sizes and the number of subdomains in the case of generous overlap.

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Additional Information

**Susanne C. Brenner**

Affiliation:
Department of Mathematics and Computer Science, Clarkson University, Potsdam, New York 13699-5815

Address at time of publication:
Department of Mathematics, University of South Carolina, Columbia, South Carolina 29208

Email:
brenner@math.sc.edu

DOI:
https://doi.org/10.1090/S0025-5718-96-00746-6

Keywords:
Domain decomposition,
additive Schwarz preconditioner,
nonconforming finite elements,
Laplace equation,
biharmonic equation,
stationary Stokes equations

Received by editor(s):
July 6, 1993

Received by editor(s) in revised form:
November 18, 1993, and August 1, 1994

Additional Notes:
This work was supported in part by the National Science Foundation under Grant No. DMS-92-09332.

Article copyright:
© Copyright 1996
American Mathematical Society