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Adaptive coupling of FEM and BEM: Simple error estimators and convergence
Author(s) -
Aurada Markus,
Feischl Michael,
Karkulik Michael,
Praetorius Dirk
Publication year - 2011
Publication title -
pamm
Language(s) - English
Resource type - Journals
ISSN - 1617-7061
DOI - 10.1002/pamm.201110367
Subject(s) - estimator , finite element method , a priori and a posteriori , convergence (economics) , coupling (piping) , mathematics , computer science , boundary element method , adaptive mesh refinement , simple (philosophy) , mathematical optimization , boundary (topology) , adaptive algorithm , algorithm , mathematical analysis , computational science , engineering , mechanical engineering , structural engineering , statistics , economics , philosophy , epistemology , economic growth
A posteriori error estimators and adaptive mesh‐refinement have themselves proven to be important tools for scientific computing. For error control in finite element methods (FEM), there is a broad variety of a posteriori error estimators available, and convergence as well as optimality of adaptive FEM is well‐studied in the literature. This is, however, in sharp contrast to the boundary element method (BEM) and to the coupling of FEM and BEM. In our contribution, we present an easy‐to‐implement error estimator for some FEM‐BEM coupling which, to the best of our knowledge, has not been proposed in the literature before. The derived mesh‐refining algorithm provides the first adaptive coupling procedure which is mathematically proven to converge. (© 2011 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)