Mathematics of Computation

Two-level Additive Schwarz Preconditioners for Nonconforming Finite Element Methods

Author(s): Susanne C. Brenner.
Journal: Math. Comp. 65 (1996), 897-921.
MSC (1991): Primary 65F10, 65N30, 65N55
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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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Retrieve articles in Mathematics of Computation with MSC (1991): 65F10, 65N30, 65N55

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: 10.1090/S0025-5718-96-00746-6
PII: S 0025-5718(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.
Copyright of article: Copyright 1996, American Mathematical Society

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