AN A-POSTERIORI ERROR ESTIMATOR FOR THE STABLE GENERALIZED/EXTENDED FINITE ELEMENT METHOD
Rafael Marques Lins1; Sergio Persival Baroncini Proença1; Carlos Armando Magalhães Duarte2
1 University of São Paulo (USP); 2 University of Illinois at Urbana-Champaign
doi:10.20906/CPS/CILAMCE2017-0868
Resumo
This study investigates the performance of a recovery-based a-posteriori error estimator in the framework of the Stable Generalized FEM (SGFEM). Different types of enrichment functions can be considered. When applied to linear Fracture Mechanics problems, this estimator is based on a splitting of the recovered stress field into two distinct parts: singular and smooth. The singular part is computed with the help of asymptotic expansions of the stress field nearby the crack tip, whereas the recovered smooth one is calculated from a combination between the Superconvergent Patch Recovery (SPR) and Singular Value Decomposition (SVD) techniques. Two numerical examples are selected to assess the robustness of the error estimator considering polynomial and special enrichment functions in two-dimensional analysis. Therefore, relevant aspects such as effectivity indexes, error distribution and convergence rates are used for assessing the error estimator. The main conclusion of this study is that the error estimator hereby developed can provide accurate results for both the GFEM and SGFEM. In particular, this feature can be used to verify the efficacy of the SGFEM even in problems without analytical solutions.
Palavras-chave: Error estimation; Generalized FEM; Effectivity index; Fracture