Optimal-order nonnested multigrid methods for solving finite element equations III: on degenerate meshes

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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