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Bounds for quantities of interest and adaptivity in the element‐free Galerkin method
Author(s) -
Vidal Yolanda,
Parés Núria,
Díez Pedro,
Huerta Antonio
Publication year - 2008
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.2380
Subject(s) - estimator , domain decomposition methods , residual , convergence (economics) , simple (philosophy) , norm (philosophy) , mathematics , mathematical optimization , finite element method , effective domain , polygon mesh , computer science , method of mean weighted residuals , algorithm , domain (mathematical analysis) , galerkin method , mathematical analysis , geometry , regular polygon , philosophy , law , economic growth , epistemology , political science , thermodynamics , statistics , physics , economics , convex optimization , convex combination
Abstract A novel approach to implicit residual‐type error estimation in mesh‐free methods and an adaptive refinement strategy are presented. This allows computing upper and lower bounds of the error in energy norm with the ultimate goal of obtaining bounds for outputs of interest. The proposed approach precludes the main drawbacks of standard residual‐type estimators circumventing the need of flux‐equilibration and resulting in a simple implementation that avoids integrals on edges/sides of a domain decomposition (mesh). This is especially interesting for mesh‐free methods. The adaptive strategy proposed leads to a fast convergence of the bounds to the desired precision. Copyright © 2008 John Wiley & Sons, Ltd.