An a-posteriori error estimator for linear elastic fracture mechanics using the stable generalized/extended finite element method

DOI10.1007/s00466-015-1212-8zbMath1336.74067OpenAlexW1820610762WikidataQ113327590 ScholiaQ113327590MaRDI QIDQ905052

R. M. Lins, M. D. C. Ferreira, S. P. B. Proença, C. Armando Duarte

Publication date: 14 January 2016

Published in: Computational Mechanics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s00466-015-1212-8

zbMATH Keywords

error estimationextended FEMgeneralized FEMeffectivity indexblending elements

Mathematics Subject Classification ID

Classical linear elasticity (74B05) Brittle fracture (74R10) Finite element methods applied to problems in solid mechanics (74S05) Error bounds for boundary value problems involving PDEs (65N15) Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs (65N30)

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Uses Software

• XFEM

Cites Work

• Unnamed Item
• Stable generalized finite element method (SGFEM)
• Derivative recovery and a posteriori error estimate for extended finite elements
• A posteriori error estimation in finite element analysis
• The partition of unity finite element method: basic theory and applications
• Generalized finite element method in structural nonlinear analysis -- a \(p\)-adaptive strategy
• A stable and optimally convergent generalized FEM (SGFEM) for linear elastic fracture mechanics
• The extended/generalized finite element method: An overview of the method and its applications
• Improving the accuracy of XFEM crack tip fields using higher order quadrature and statically admissible stress recovery
• Integration of singular enrichment functions in the generalized/extended finite element method for three-dimensional problems
• Blending in the extended finite element method by discontinuous Galerkin and assumed strain methods
• A corrected XFEM approximation without problems in blending elements
• A recovery-type error estimator for the extended finite element method based onsingular+smoothstress field splitting
• Enhanced blending elements for XFEM applied to linear elastic fracture mechanics
• A simple error estimator and adaptive procedure for practical engineerng analysis
• A Mixed-Mode Crack Analysis of Isotropic Solids Using Conservation Laws of Elasticity
• The superconvergent patch recovery anda posteriori error estimates. Part 1: The recovery technique
• The superconvergent patch recovery anda posteriori error estimates. Part 2: Error estimates and adaptivity
• Practical aspects of a-posteriori estimation for reliable finite element analysis
• Elastic crack growth in finite elements with minimal remeshing
• Patch recovery based on superconvergent derivatives and equilibrium
• THE PARTITION OF UNITY METHOD
• On the construction of blending elements for local partition of unity enriched finite elements
• A finite element method for crack growth without remeshing
• A simple error estimator for extended finite elements
• High-order extended finite element method for cracked domains
• GENERALIZED FINITE ELEMENT METHODS — MAIN IDEAS, RESULTS AND PERSPECTIVE
• The generalized finite element method

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