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A p ‐adaptive algorithm for the BEM with the hypersingular operator on the plane screen
Author(s) -
Heuer Norbert,
Mellado Mario E.,
Stephan Ernst P.
Publication year - 2001
Publication title -
international journal for numerical methods in engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.421
H-Index - 168
eISSN - 1097-0207
pISSN - 0029-5981
DOI - 10.1002/nme.393
Subject(s) - ansatz , estimator , mathematics , linear subspace , galerkin method , operator (biology) , algorithm , laplace operator , polynomial , space (punctuation) , plane (geometry) , decomposition , finite element method , mathematical analysis , computer science , geometry , physics , chemistry , gene , transcription factor , mathematical physics , thermodynamics , operating system , ecology , biology , biochemistry , statistics , repressor
We propose a p ‐adaptive algorithm for the Galerkin method solving the hypersingular integral operator of the Laplacian on the plane screen. The error indicators/estimators are based on projections of the actual error onto local subspaces. These subspaces are defined by decompositions of specially designed enriched ansatz spaces. Our algorithm uses different strategies for the refinement and the stopping criterion. The error estimator that stops the algorithm is based on an overlapping decomposition of an ansatz space that is defined by mesh refinement. The error indicators that steer the p ‐refinement are computed via an almost direct decomposition of an enriched ansatz space that uses the same mesh but higher polynomial degrees. Numerical results support the efficiency of our algorithm. Copyright © 2001 John Wiley & Sons, Ltd.