Local a-posteriori error indicators for the Galerkin discretization of boundary integral equations

descriptionPublicationkeyboard_double_arrow_right Article 01 Mar 1998Publisher:Springer Science and Business Media LLCJournal:Numerische Mathematik, volume 79, pages 43-76 (issn: 0029-599X, eissn: 0945-3245,

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Authors: Faermann, Birgit;

doi: 10.1007/s002110050331

Local a-posteriori error indicators for the Galerkin discretization of boundary integral equations

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Abstract

The error indicators of \textit{I. Babuška} and \textit{W. C. Rheinboldt} [SIAM J. Numer. Anal. 15, 736-754 (1978; Zbl 0398.65069)] are transferred from finite element methods onto boundary element methods in the two- and three-dimensional case. It is shown that they are reliable and efficient for a wide class of integral operators under relatively weak assumptions. The proofs contain sophisticated estimates for norms in Sobolev spaces with fractional order.

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Kiel University
Germany

Keywords

error indicators, Error bounds for boundary value problems involving PDEs, Boundary value problems for second-order elliptic equations, boundary element methods, Sobolev spaces with fractional order, boundary integral equations, Boundary element methods for boundary value problems involving PDEs, Mesh generation, refinement, and adaptive methods for boundary value problems involving PDEs, Galerkin method

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