Efficient and accurate stress recovery procedure and a posteriori error estimator for the stable generalized/extended finite element method

Summary This paper presents a new stress recovery technique for the generalized/extended finite element method (G/XFEM) and for the stable generalized FEM (SGFEM). The recovery procedure is based on a locally weighted L2 projection of raw stresses over element patches; the set of elements sharing a...

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Bibliographic Details
Published in:International journal for numerical methods in engineering Vol. 119; no. 12; pp. 1279 - 1306
Main Authors: Lins, Rafael, Proença, Sergio Persival, Duarte, C. Armando
Format: Journal Article
Language:English
Published: Bognor Regis Wiley Subscription Services, Inc 21.09.2019
Subjects:
error estimation
extended FEM
Finite element analysis
Finite element method
generalized FEM
Nonlinear programming
Recovery
smoothing
stress recovery
Stresses
ISSN:0029-5981, 1097-0207
Online Access:Get full text
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Summary:Summary This paper presents a new stress recovery technique for the generalized/extended finite element method (G/XFEM) and for the stable generalized FEM (SGFEM). The recovery procedure is based on a locally weighted L2 projection of raw stresses over element patches; the set of elements sharing a node. Such projection leads to a block‐diagonal system of equations for the recovered stresses. The recovery procedure can be used with GFEM and SGFEM approximations based on any choice of elements and enrichment functions. Here, the focus is on low‐order 2D approximations for linear elastic fracture problems. A procedure for computing recovered stresses at re‐entrant corners of any internal angle is also presented. The proposed stress recovery technique is used to define a Zienkiewicz‐Zhu (ZZ) a posteriori error estimator for the G/XFEM and the SGFEM. The accuracy, computational cost, and convergence rate of recovered stresses together with the quality of the ZZ estimator, including its effectivity index, are demonstrated in problems with smooth and singular solutions.
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ISSN:0029-5981
1097-0207
DOI:10.1002/nme.6091