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Mathematics of Computation

ISSN 1088-6842(online) ISSN 0025-5718(print)

 
 

 

Convergence
of nonconforming multigrid methods
without full elliptic regularity


Author: Susanne C. Brenner
Journal: Math. Comp. 68 (1999), 25-53
MSC (1991): Primary 65N55, 65N30
DOI: https://doi.org/10.1090/S0025-5718-99-01035-2
MathSciNet review: 1620215
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Abstract: We consider nonconforming multigrid methods for symmetric positive definite second and fourth order elliptic boundary value problems which do not have full elliptic regularity. We prove that there is a bound ($<1$) for the contraction number of the $W$-cycle algorithm which is independent of mesh level, provided that the number of smoothing steps is sufficiently large. We also show that the symmetric variable $V$-cycle algorithm is an optimal preconditioner.


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Additional Information

Susanne C. Brenner
Affiliation: Department of Mathematics, University of South Carolina, Columbia, SC 29208
Email: brenner@math.sc.edu

DOI: https://doi.org/10.1090/S0025-5718-99-01035-2
Keywords: Multigrid methods, nonconforming finite elements, macro elements, precondi\-tion\-er, $W$-cycle, variable $V$-cycle
Received by editor(s): April 13, 1995
Additional Notes: This work was supported in part by the National Science Foundation under Grant No. DMS-94-96275.
Article copyright: © Copyright 1999 American Mathematical Society