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Mathematics of Computation

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Optimal-order nonnested multigrid methods for solving finite element equations. III. On degenerate meshes

Author: Shangyou Zhang
Journal: Math. Comp. 64 (1995), 23-49
MSC: Primary 65N30; Secondary 65F10
MathSciNet review: 1257583
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Abstract: In this paper, we consider several model problems where finite element triangular meshes with arbitrarily small angles (high aspect ratios) are utilized to deal with anisotropy, interfaces, or singular perturbations. The constant-rate (independent of the number of unknowns, the smallest angle, the interface discontinuity, the singular-perturbation parameter, etc.) convergence of some special nonnested multigrid methods for solving the finite element systems on such degenerate meshes will be proved. Numerical data are provided to support the analysis in each case.

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Article copyright: © Copyright 1995 American Mathematical Society

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