Analysis of V-cycle multigrid algorithms for forms defined by numerical quadrature

Journal Article · Sun May 01 04:00:00 EDT 1994 · SIAM Journal on Scientific and Statistical Computing (Society for Industrial and Applied Mathematics); (United States)

DOI:https://doi.org/10.1137/0915037· OSTI ID:7041547

Bramble, J H ^[1]; Goldstein, C I; Pasciak, J E ^[2]

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1. Cornell Univ., Ithaca, NY (United States). Dept. of Mathematics
2. Brookhaven National Lab., Long Island, NY (United States). Applied Mathematics Dept.

The authors describe and analyze certain V-cycle multigrid algorithms with forms defined by numerical quadrature applied to the approximation of symmetric second-order elliptic boundary value problems. This approach can be used for the efficient solution of finite element systems resulting from numerical quadrature as well as systems arising from finite difference discretizations. The results are based on a regularity free theory and hence apply to meshes with local grid refinement as well as the quasi-uniform case. It is shown that uniform (independent of the number of levels) convergence rates often hold for appropriately defined V-cycle algorithms with as few as one smoothing per grid. These results hold even on applications without full elliptic regularity, e.g., a domain in R[sup 2] with a crack.

• DOE Contract Number: AC02-76CH00016
• OSTI ID: 7041547
• Journal Information: SIAM Journal on Scientific and Statistical Computing (Society for Industrial and Applied Mathematics); (United States), Journal Name: SIAM Journal on Scientific and Statistical Computing (Society for Industrial and Applied Mathematics); (United States) Vol. 15:3; ISSN 0196-5204; ISSN SIJCD4
• Country of Publication: United States
• Language: English

Related Subjects

99 GENERAL AND MISCELLANEOUS
990200* -- Mathematics & Computers
ALGORITHMS
BOUNDARY-VALUE PROBLEMS
CALCULATION METHODS
CONVERGENCE
DIFFERENTIAL EQUATIONS
EQUATIONS
FINITE ELEMENT METHOD
MATHEMATICAL LOGIC
MESH GENERATION
NUMERICAL SOLUTION
PARTIAL DIFFERENTIAL EQUATIONS
QUADRATURES