Error estimation for proper generalized decomposition solutions: A dual approach

descriptionPublicationkeyboard_double_arrow_right Article 04 Aug 2020 Spain English Publisher:WileyJournal:International Journal for Numerical Methods in Engineering, volume 121, pages 5,275-5,294 (issn: 0029-5981, eissn: 1097-0207,

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Authors: Reis, Jonatha; Moitinho de Almeida, J. P.; Díez, Pedro; Zlotnik, Sergio;

doi: 10.1002/nme.6452

handle: 2117/343733

Error estimation for proper generalized decomposition solutions: A dual approach

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Abstract

SummaryThe proper generalized decomposition is a well‐established reduced order method, used to efficiently obtain approximate solutions of multi‐dimensional problems in a procedure that controls the effects of the “curse of dimensionality.” The question of assessing the quality of the solutions obtained and adapting the approximations assumed, for example, the finite element meshes used, so that the best result is obtained at minimal cost, remains a relevant challenge. This article deals with finite element solutions for solid mechanics problems, using the error obtained from a dual analysis, the difference between complementary solutions, to bound the error in the solutions and to drive an optimal adaptivity process, which obtains meshes with errors significantly lower than those obtained using a uniform refinement.

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Spain

Related Organizations

Universidade de Lisboa
Portugal
Universitat Politècnica de Catalunya
Spain
Universidade de Lisboa
Portugal
University of Lisbon
Portugal
Universitat Polite`cnica de Catalunya
Spain

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Keywords

:65 Numerical analysis::65G Error analysis and interval analysis [Classificació AMS], Anàlisi numèrica, 330, Error bounds for boundary value problems involving PDEs, Model reduction, Proper generalized decomposition, :Matemàtiques i estadística::Anàlisi numèrica::Mètodes numèrics [Àrees temàtiques de la UPC], Numerical methods for partial differential equations, boundary value problems, Equilibrium formulation, error bounds, Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs, 510, Classificació AMS::65 Numerical analysis::65G Error analysis and interval analysis, Error bounds, Error estimation, equilibrium formulation, error estimation, model reduction, proper generalized decomposition, Àrees temàtiques de la UPC::Matemàtiques i estadística::Anàlisi numèrica::Mètodes numèrics, Numerical analysis

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