Extrapolation techniques for reducing the pollution effect of reentrant corners in the finite element method

DOI10.1007/BF01400891zbMath0649.65060MaRDI QIDQ1106002

Heribert Blum, Rolf Rannacher

Publication date: 1988

Published in: Numerische Mathematik (Search for Journal in Brave)

Full work available at URL: https://eudml.org/doc/133252

zbMATH Keywords

singularitiesnumerical examplesLaplace equationextrapolationFinite elementreentrant cornersasymptotic error representationRayleigh-Ritz and Galerkin methods

Mathematics Subject Classification ID

Finite element methods applied to problems in solid mechanics (74S05) 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) Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation (35J05)

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Cascadic multigrid methods combined with sixth order compact scheme for Poisson equation ⋮ Error estimates of finite element method about elliptic problems with singular righthand side ⋮ Accuracy analysis of the Adini element for biharmonic equation ⋮ Extrapolation of numerical solutions for elliptic problems on corner domains ⋮ Recovery and few parameter representation of the optimal mesh density function for near optimal finite element meshes ⋮ High effective finite element algorithm for elliptic partial differential equation ⋮ The extrapolation of numerical eigenvalues by finite elements for differential operators ⋮ The optimal convergence of finite element methods for the three-dimensional second-order elliptic boundary value problem with singularity ⋮ An Extrapolation Cascadic Multigrid Method for Elliptic Problems on Reentrant Domains ⋮ Extrapolation of the Hood-Taylor elements for the Stokes problem ⋮ The role of surface tension in the dominant balance in the die swell singularity ⋮ Finite element approximations for \(\Delta u-qu=f\) on a Riemann surface ⋮ Singularities and treatments of elliptic boundary value problems.

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