Adaptive FEM-BEM coupling with a Schur complement error indicator
type: Item
instance of: scholarly article
title: Adaptive FEM-BEM coupling with a Schur complement error indicator
zbMATH Open document ID: 1202.65155
author: A. Krebs
author: Matthias Maischak
author: Ernst P. Stephan
published in: Applied Numerical Mathematics
publication date: 2010-06-25T00:00:00Z
review text: An interface problem in two dimensions with and inhomogeneous partial differential equation in the interior domain and a homogeneous partial differential equation in the exterior domain is considered. A symmetric coupling method and a Galerkin scheme are applied which yield a coupled set of finite element-boundary element equations. The Steklov-Poincaré operator is discretized using stable hierarchical basis decompositions for finite elements. It is shown that the two-level additive Schwarz operator has a bounded condition number. An a posteriori error estimate is derived with local error indicators. An adaptive algorithm to compute the finite element solution on a sequence of locally refined meshes in the interior domain and on the interface boundary is also presented. Finally, numerical experiments of a nonlinear interface problem in a L-shaped domain illustrate the reliability of the error indicators.
reviewed by: Kai Schneider
Mathematics Subject Classification ID: 65N30
Mathematics Subject Classification ID: 65N38
Mathematics Subject Classification ID: 35J65
Mathematics Subject Classification ID: 65N15
zbMATH DE Number: 5726717
zbMATH Keywords: adaptive finite element methods
zbMATH Keywords: adaptive boundary element methods
zbMATH Keywords: a-posteriori error estimate
zbMATH Keywords: Steklov-Poincaré operator
zbMATH Keywords: hierarchical basis
zbMATH Keywords: Galerkin scheme
zbMATH Keywords: two-level additive Schwarz operator
zbMATH Keywords: condition number
zbMATH Keywords: algorithm
zbMATH Keywords: numerical experiments
zbMATH Keywords: nonlinear interface problem
MaRDI profile type: Publication
full work available at URL: j.apnum.2010.04.004
OpenAlex ID: W2062359704
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DOI: 10.1016/J.APNUM.2010.04.004
description: scientific article; zbMATH DE number 5726717