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An Optimal Order Nonnested Mixed Multigrid Method for Generalized Stokes ProblemsA multigrid algorithm is developed and analyzed for generalized Stokes problems discretized by various nonnested mixed finite elements within a unified framework. It is abstractly proved by an element-independent analysis that the multigrid algorithm converges with an optimal order if there exists a 'good' prolongation operator. A technique to construct a 'good' prolongation operator for nonnested multilevel finite element spaces is proposed. Its basic idea is to introduce a sequence of auxiliary nested multilevel finite element spaces and define a prolongation operator as a composite operator of two single grid level operators. This makes not only the construction of a prolongation operator much easier (the final explicit forms of such prolongation operators are fairly simple), but the verification of the approximate properties for prolongation operators is also simplified. Finally, as an application, the framework and technique is applied to seven typical nonnested mixed finite elements.
Document ID
19970006875
Acquisition Source
Langley Research Center
Document Type
Conference Paper
Authors
Deng, Qingping
(Tennessee Univ. Knoxville, TN United States)
Date Acquired
August 17, 2013
Publication Date
September 1, 1996
Publication Information
Publication: Seventh Copper Mountain Conference on Multigrid Methods
Issue: Part 1
Subject Category
Computer Programming And Software
Accession Number
97N13768
Distribution Limits
Public
Copyright
Work of the US Gov. Public Use Permitted.
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