Bounds for quantities of interest and adaptivity in the element‐free Galerkin method |
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Authors: | Yolanda Vidal Núria Parés Pedro Díez Antonio Huerta |
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Affiliation: | Departament de Matemàtica Aplicada III, Laboratori de Càlcul Numèric (LaCàN), Universitat Politècnica de Catalunya, Jordi Girona 1, E‐08034 Barcelona, Spain |
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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. |
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Keywords: | element‐free Galerkin mesh‐free error estimation engineering outputs functional outputs goal‐oriented error estimation residual‐based estimators adaptivity |
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