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Strict error bounds for linear and nonlinear solid mechanics problems using a patch-based flux-free method Cottereau, Regis Chamoin, Ludovic Díez, Pedro Universitat Politècnica de Catalunya. Departament de Matemàtica Aplicada III Universitat Politècnica de Catalunya. LACÀN - Mètodes Numèrics en Ciències Aplicades i Enginyeria Àrees temàtiques de la UPC::Matemàtiques i estadística::Anàlisi numèrica::Mètodes en elements finits Finite element method Continuum mechanics Partial differential equations Elements finits, Mètode dels Mecànica dels sòlids Equacions diferencials We discuss, in this paper, a common ux-free method for the computation of strict error bounds for linear and nonlinear Finite Element computations. In the linear case, the error bounds are on the energy norm of the error, while, in the nonlinear case, the concept of error in constitutive relation is used. In both cases, the error bounds are strict in the sense that they re- fer to the exact solution of the continuous equations, rather than to some FE computation over a refined mesh. For both linear and nonlinear solid mechanics, this method is based on the computation of a statically admissible stress field, which is performed as a series of local problems on patches of elements. There is no requirement to solve a previous problem of ux equilibration globally, as happens with other methods. Postprint (published version) 2010-12 Article Cottereau, R.; Chamoin, L.; Díez, P. Strict error bounds for linear and nonlinear solid mechanics problems using a patch-based flux-free method. "Mecanique and industries", Desembre 2010, vol. 11, núm. 3-4, p. 249-254. 1296-2139 https://hdl.handle.net/2117/12191 10.1051/meca/2010049 eng http://www-lacan.upc.edu/publications/files/MeI_RCx_LCx_PDM_2010.pdf http://creativecommons.org/licenses/by-nc-nd/3.0/es/ Open Access Attribution-NonCommercial-NoDerivs 3.0 Spain 6 p. application/pdf