A posteriori error analysis for elliptic PDEs on domains with complicated structures

DOI10.1007/s00211-003-0495-4zbMath1049.65120OpenAlexW2064700919MaRDI QIDQ1434057

Carsten Carstensen, Stefan A. Sauter

Publication date: 1 July 2004

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

Full work available at URL: https://www.zora.uzh.ch/id/eprint/21775/1/10-01.pdf

zbMATH Keywords

finite element methodboundary value problemmixed boundary conditionsPoisson problema posteriori error estimationsextension operatorstrace theoremsPoincare inequalitiescomplicated domainsconforming piecewise affine elements

Mathematics Subject Classification ID

Error bounds for boundary value problems involving PDEs (65N15) 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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Explicit constants in Poincaré-type inequalities for simplicial domains and application to a posteriori estimates ⋮ Adaptive discontinuous Galerkin methods for elliptic interface problems ⋮ The approximation and computation of a basis of the trace space \(H^{1/2}\) ⋮ Analysis-aware defeaturing: Problem setting and a posteriori estimation ⋮ Saturation estimates for \(hp\)-finite element methods ⋮ Geometric transformation of finite element methods: theory and applications ⋮ Functional a posteriori error estimates for problems with nonlinear boundary conditions ⋮ A posteriori error estimation for the Poisson equation with mixed Dirichlet/Neumann boundary conditions. ⋮ Finite element methods for the Stokes problem on complicated domains ⋮ A posteriori error estimation of goal-oriented quantities for elliptic type BVPs ⋮ ℎ𝑝-version discontinuous Galerkin methods on essentially arbitrarily-shaped elements

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