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Error indicators for adaptive mesh refinement in the boundary element method—a new approach
Author(s) -
Guiggiani Massimo
Publication year - 1990
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.1620290610
Subject(s) - pointwise , a priori and a posteriori , collocation (remote sensing) , computer science , adaptive mesh refinement , boundary (topology) , polygon mesh , boundary element method , convergence (economics) , finite element method , mesh generation , algorithm , process (computing) , mathematical optimization , cauchy distribution , mathematics , computational science , mathematical analysis , structural engineering , philosophy , computer graphics (images) , epistemology , machine learning , engineering , economics , economic growth , operating system
In this paper a new approach to the development of a posteriori error indicators for the direct boundary element method (BEM) is presented. It takes advantage of a unique opportunity offered by the collocation BEM, that is the possibility of obtaining more than one numerical solution from a given boundary element mesh. Unlike other approaches, the error indicator introduced in the present paper does not require any explicit evaluation of the residual of the approximate solution. In order to test the capability of the proposed error indicators to actually control a selective mesh refinement process, an h ‐adaptive refinement strategy is also described, together with the criteria for refinement and for the termination of the adaptive process. Full details on the whole numerical implementation for two‐dimensional problems are provided. In particular, there is described a direct method for the numerical evaluation of Cauchy principal value integrals. Numerical examples show that pointwise convergence is always obtained in a few steps and the final meshes look nearly as if they were designed by an expert analyst.