Bounds for quantities of interest and adaptivity in the element‐free Galerkin method

descriptionPublicationkeyboard_double_arrow_right Article 10 Jul 2008 Spain English Publisher:WileyJournal:International Journal for Numerical Methods in Engineering, volume 76, pages 1,782-1,818 (issn: 0029-5981, eissn: 1097-0207,

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Authors: Vidal Seguí, Yolanda; Parés Mariné, Núria; Díez, Pedro; Huerta, Antonio;

doi: 10.1002/nme.2380

handle: 2117/8160

Bounds for quantities of interest and adaptivity in the element‐free Galerkin method

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Abstract

AbstractA 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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Spain

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Keywords

Engineering, Civil, Engineering, Multidisciplinary, functional outputs, Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs, element-free Galerkin, adaptivity, Diffusion and convection, Mètodes de, Galerkin, Mètodes de, Engineering, Ocean, Engineering, Aerospace, Engineering, Biomedical, Àrees temàtiques de la UPC::Matemàtiques i estadística::Anàlisi numèrica::Mètodes numèrics, mesh-free, Error bounds for boundary value problems involving PDEs, Other numerical methods (fluid mechanics), :Matemàtiques i estadística::Anàlisi numèrica::Mètodes numèrics [Àrees temàtiques de la UPC], Galerkin, residual-based estimators, Computer Science, Software Engineering, Engineering, Marine, Galerkin methods, Engineering, Manufacturing, Engineering, Mechanical, goal-oriented error estimation, error estimation, Engineering, Industrial, engineering outputs

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