Multigrid Methods for Anisotropic Edge Refinement

DOI10.1137/S0036142900375414zbMath1036.65106MaRDI QIDQ4785847

Thomas Apel, Joachim Schöberl

Publication date: 5 January 2003

Published in: SIAM Journal on Numerical Analysis (Search for Journal in Brave)

zbMATH Keywords

performancecomplexityalgorithmconvergencenumerical resultsfinite element methodmultigrid methodGauss-Seidel iterationanisotropic meshedge singularityline Jacobi smoother

Mathematics Subject Classification ID

Multigrid methods; domain decomposition for boundary value problems involving PDEs (65N55) Boundary value problems for second-order elliptic equations (35J25) Stability and convergence of numerical methods for boundary value problems involving PDEs (65N12) Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs (65N30) Iterative numerical methods for linear systems (65F10) Mesh generation, refinement, and adaptive methods for boundary value problems involving PDEs (65N50) Complexity and performance of numerical algorithms (65Y20)

Related Items (12)

A new methodology for anisotropic mesh refinement based upon error gradients ⋮ Editorial. Recent advances in finite element methods ⋮ Condition numbers of finite element methods on a class of anisotropic meshes ⋮ On the robustness of a multigrid method for anisotropic reaction-diffusion problems ⋮ An anisotropic finite element method on polyhedral domains: Interpolation error analysis ⋮ Hierarchical decomposition of domains with fractures ⋮ Regularity and a priori error analysis on anisotropic meshes of a Dirichlet problem in polyhedral domains ⋮ A priori analysis of an anisotropic finite element method for elliptic equations in polyhedral domains ⋮ Multilevel methods for nonuniformly elliptic operators and fractional diffusion ⋮ An efficient interpolation algorithm on anisotropic grids for functions with jump discontinuities in 2-D ⋮ Optimal anisotropic meshes for minimizing interpolation errors in $L^p$-norm ⋮ Graded mesh approximation in weighted Sobolev spaces and elliptic equations in 2D

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