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Dual boundary‐element method: Simple error estimator and adaptivity
Author(s) -
Portela A.
Publication year - 2011
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.3119
Subject(s) - discontinuity (linguistics) , boundary element method , estimator , collocation (remote sensing) , boundary (topology) , degenerate energy levels , simple (philosophy) , mathematics , parametric statistics , parametric equation , dual (grammatical number) , finite element method , singular boundary method , mathematical analysis , computer science , geometry , structural engineering , engineering , philosophy , statistics , physics , epistemology , quantum mechanics , machine learning , art , literature
Abstract This paper is concerned with the effective numerical implementation of the adaptive dual boundary‐element method (DBEM), for two‐dimensional potential problems. Two boundary integral equations, which are the potential and the flux equations, are applied for collocation along regular and degenerate boundaries, leading always to a single‐region analysis. Taking advantage on the use of non‐conforming parametric boundary‐elements, the method introduces a simple error estimator, based on the discontinuity of the solution across the boundaries between adjacent elements and implements the p , h and mixed versions of the adaptive mesh refinement. Examples of several geometries, which include degenerate boundaries, are analyzed with this new formulation to solve regular and singular problems. The accuracy and efficiency of the implementation described herein make this a reliable formulation of the adaptive DBEM. Copyright © 2011 John Wiley & Sons, Ltd.