Energy norm based a posteriori error estimation for boundary element methods in two dimensions

DOI10.1016/j.apnum.2008.12.024zbMath1177.65192OpenAlexW1983910603MaRDI QIDQ842936

Dirk Praetorius, Christoph Erath, Samuel Ferraz-Leite, Stefan A. Funken

Publication date: 28 September 2009

Published in: Applied Numerical Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.apnum.2008.12.024

zbMATH Keywords

Galerkin methodnumerical experimentsLaplace equationsingular integral equationerror estimatorsboundary elements methodsimple layer potentialexterior Navier-Lame problem

Mathematics Subject Classification ID

Numerical methods for integral equations (65R20) Error bounds for boundary value problems involving PDEs (65N15) Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation (35J05) Integral equations of the convolution type (Abel, Picard, Toeplitz and Wiener-Hopf type) (45E10) Boundary element methods for boundary value problems involving PDEs (65N38)

Related Items (21)

HILBERT -- a MATLAB implementation of adaptive 2D-BEM. \(\underline {\text H}\)ilbert \(\underline {\text I}\)s a \(\underline {\text L}\)ovely \(\underline {\text B}\)oundary \(\underline {\text E}\)lement \(\underline {\text R}\)esearch \(\underline {\text T}\)ool ⋮ Simple a posteriori error estimators for the \(h\)-version of the boundary element method ⋮ Adaptive boundary element methods with convergence rates ⋮ \(hp\)-adaptive IPDG/TDG-FEM for parabolic obstacle problems ⋮ Adaptive boundary element methods. A posteriori error estimators, adaptivity, convergence, and implementation ⋮ A new conservative numerical scheme for flow problems on unstructured grids and unbounded domains ⋮ Two-level error estimation for the integral fractional Laplacian ⋮ Convergence of adaptive BEM for some mixed boundary value problem ⋮ Estimator reduction and convergence of adaptive BEM ⋮ Convergence of adaptive boundary element methods ⋮ A posteriori error estimates for the Johnson-Nédélec FEM-BEM coupling ⋮ A posteriori error estimates of \(hp\)-adaptive IPDG-FEM for elliptic obstacle problems ⋮ A new error estimation approach based on fuzzy logic system for H-R adaptive boundary element method ⋮ ZZ-type a posteriori error estimators for adaptive boundary element methods on a curve ⋮ Convergence and quasi-optimality of adaptive FEM with inhomogeneous Dirichlet data ⋮ A posteriori error analysis for a boundary element method with nonconforming domain decomposition ⋮ Functional a posteriori error estimates for boundary element methods ⋮ The saturation assumption yields optimal convergence of two-level adaptive BEM ⋮ A Posteriori Error Estimates for the Electric Field Integral Equation on Polyhedra ⋮ Simple error estimators for the Galerkin BEM for some hypersingular integral equation in 2D ⋮ Adaptive Crouzeix–Raviart boundary element method

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