A constructive a priori error estimation for finite element discretizations in a non-convex domain using singular functions

DOI10.1007/BF03186546zbMath1186.65143OpenAlexW2169092453MaRDI QIDQ849195

Kenta Kobayashi

Publication date: 25 February 2010

Published in: Japan Journal of Industrial and Applied Mathematics (Search for Journal in Brave)

Full work available at URL: https://projecteuclid.org/euclid.jjiam/1265033793

zbMATH Keywords

convergencefinite element methodnumerical examplesPoisson equationre-entrant cornerssingular functionsa priori error estimationH-shaped domainsL-shaped domains

Mathematics Subject Classification ID

Error bounds for boundary value problems involving PDEs (65N15) 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) Mesh generation, refinement, and adaptive methods for boundary value problems involving PDEs (65N50)

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Cites Work

• Numerical verifications of solutions for nonlinear elliptic equations
• Direct and inverse error estimates for finite elements with mesh refinements
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• On the use of singular functions with finite element approximations
• A Finite Element Method Using Singular Functions for the Poisson Equation: Corner Singularities
• Coefficients of the Singularities for Elliptic Boundary Value Problems on Domains with Conical Points. III: Finite Element Methods on Polygonal Domains
• Multigrid methods for the computation of singular solutions and stress intensity factors I: Corner singularities
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