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Mathematics of Computation
Mathematics of Computation
ISSN 1088-6842(online) ISSN 0025-5718(print)

 

Convergence of the multigrid $V$-cycle algorithm for second-order boundary value problems without full elliptic regularity


Author: Susanne C. Brenner
Journal: Math. Comp. 71 (2002), 507-525
MSC (2000): Primary 65N55, 65N30
Published electronically: November 19, 2001
MathSciNet review: 1885612
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Abstract: The multigrid $V$-cycle algorithm using the Richardson relaxation scheme as the smoother is studied in this paper. For second-order elliptic boundary value problems, the contraction number of the $V$-cycle algorithm is shown to improve uniformly with the increase of the number of smoothing steps, without assuming full elliptic regularity. As a consequence, the $V$-cycle convergence result of Braess and Hackbusch is generalized to problems without full elliptic regularity.


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Additional Information

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

DOI: http://dx.doi.org/10.1090/S0025-5718-01-01361-8
PII: S 0025-5718(01)01361-8
Keywords: $V$-cycle multigrid algorithm, second-order boundary value problems without full elliptic regularity
Received by editor(s): August 18, 1999
Received by editor(s) in revised form: October 27, 1999, and July 10, 2000
Published electronically: November 19, 2001
Additional Notes: This work was supported in part by the National Science Foundation under Grant Nos. DMS-96-00133 and DMS-00-74246.
Article copyright: © Copyright 2001 American Mathematical Society