The Convergence of Multi-Level Methods for Solving Finite-Element Equations in the Presence of Singularities

DOI10.2307/2008163zbMath0615.65115OpenAlexW4255415753MaRDI QIDQ4723224

Harry Yserentant

Publication date: 1986

Published in: Mathematics of Computation (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.2307/2008163

zbMATH Keywords

finite element methodsingularitiesmesh refinementoptimal convergence ratereentrant cornersmultigrid iteration methodmulti-level iteration method

Mathematics Subject Classification ID

Boundary value problems for second-order elliptic equations (35J25) Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs (65N30) Iterative numerical methods for linear systems (65F10) Numerical solution of discretized equations for boundary value problems involving PDEs (65N22)

Related Items (16)

On the multi-level splitting of finite element spaces ⋮ A finite element method using singular functions for Poisson equations: Mixed boundary conditions ⋮ Modified hierarchy basis for solving singular boundary value problems ⋮ Multigrid solvers for immersed finite element methods and immersed isogeometric analysis ⋮ Multigrid algorithms for symmetric discontinuous Galerkin methods on graded meshes ⋮ Multigrid methods for the symmetric interior penalty method on graded meshes ⋮ Multigrid methods for two-dimensional Maxwell's equations on graded meshes ⋮ The convergence of the cascadic conjugate-gradient method applied to elliptic problems in domains with re-entrant corners ⋮ The Analysis of Multigrid Algorithms for Nonsymmetric and Indefinite Elliptic Problems ⋮ A multilevel additive Schwarz method for a hypersingular integral equation on an open curve with graded meshes ⋮ Multigrid methods based on Hodge decomposition for a quad-curl problem ⋮ Multilevel computations of dispersed drug release ⋮ The convergence of V-cycle multigrid algorithms for axisymmetric Laplace and Maxwell equations ⋮ Singularities and treatments of elliptic boundary value problems. ⋮ Multigrid methods for the computation of singular solutions and stress intensity factors I: Corner singularities ⋮ Accuracy and adaptivity in the numerical analysis of thin-walled structures

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