Multigrid methods for saddle point problems: Stokes and Lamé systems

We develop new multigrid methods for a class of saddle point problems that include the Stokes system in fluid flow and the Lamé system in linear elasticity as special cases. The new smoothers in the multigrid methods involve optimal preconditioners for the discrete Laplace operator. We prove uniform...

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Bibliographic Details
Published inNumerische Mathematik Vol. 128; no. 2; pp. 193 - 216
Main Authors Brenner, Susanne C., Li, Hengguang, Sung, Li-Yeng
Format Journal Article
LanguageEnglish
Published Berlin/Heidelberg Springer Berlin Heidelberg 01.10.2014
Subjects
Mathematical and Computational Engineering
Mathematical and Computational Physics
Mathematical Methods in Physics
Mathematics
Mathematics and Statistics
Numerical Analysis
Numerical and Computational Physics
Simulation
Theoretical
Primary 65N55
65F10
Secondary 76D07
74B05
65N30
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Summary:We develop new multigrid methods for a class of saddle point problems that include the Stokes system in fluid flow and the Lamé system in linear elasticity as special cases. The new smoothers in the multigrid methods involve optimal preconditioners for the discrete Laplace operator. We prove uniform convergence of the W -cycle algorithm in the energy norm and present numerical results for W -cycle and V -cycle algorithms.
ISSN:0029-599X
0945-3245
DOI:10.1007/s00211-014-0607-3