An explicit residual-type error estimator for Q1-quadrilateral extended finite element method in two-dimensional linear elastic fracture mechanics

DOI10.1002/nme.3363zbMath1242.74118OpenAlexW1927560861MaRDI QIDQ2895033

Erwin Stein, Tymofiy Gerasimov, Marcus Olavi Rüter

Publication date: 2 July 2012

Published in: International Journal for Numerical Methods in Engineering (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1002/nme.3363

zbMATH Keywords

fracture mechanicsXFEMinterpolation operatorexplicit residual error estimatorbranch functions

Mathematics Subject Classification ID

Classical linear elasticity (74B05) Brittle fracture (74R10) Finite element methods applied to problems in solid mechanics (74S05)

Related Items (9)

Goal-oriented explicit residual-type error estimates in XFEM ⋮ Effects of the smoothness of partitions of unity on the quality of representation of singular enrichments for GFEM/XFEM stress approximations around brittle cracks ⋮ Pointwise dual weighted residual based goal-oriented \textit{a posteriori} error estimation and adaptive mesh refinement in 2D/3D thermo-mechanical multifield problems ⋮ An Introductory Review on A Posteriori Error Estimation in Finite Element Computations ⋮ Subdomain-based error techniques for generalized finite element approximations of problems with singular stress fields ⋮ A hierarchically enhanced recovery-based error estimator for bidimensional elastoplastic modelling by generalized finite element approach ⋮ A recovery-explicit error estimator in energy norm for linear elasticity ⋮ Residual error based adaptive mesh refinement with the non-intrusive patch algorithm ⋮ Original geometrical stopping criteria associated to multilevel adaptive mesh refinement for problems with local singularities

Cites Work

• Unnamed Item
• Unnamed Item
• Accurate recovery-based upper error bounds for the extended finite element framework
• Implicit upper bound error estimates for combined expansive model and discretization adaptivity
• Derivative recovery and a posteriori error estimate for extended finite elements
• A feedback finite element method with a posteriori error estimation. I: The finite element method and some basic properties of the a posteriori error estimator
• An equilibrium method for stress calculation using finite element displacement models
• The partition of unity finite element method: basic theory and applications
• A posteriori error estimation in large-strain elasticity using equilibrated local Neumann problems
• Anisotropic discretization- and model-error estimation in solid mechanics by local Neumann problems
• Quadrilateral mesh revisited.
• Optimal convergence analysis for the extended finite element method
• The extended/generalized finite element method: An overview of the method and its applications
• A posteriori error analysis and adaptive processes in the finite element method: Part I—error analysis
• Finite Element Interpolation of Nonsmooth Functions Satisfying Boundary Conditions
• Strict and effective bounds in goal-oriented error estimation applied to fracture mechanics problems solved with XFEM
• A corrected XFEM approximation without problems in blending elements
• Crack tip enrichment in the XFEM using a cutoff function
• A recovery-type error estimator for the extended finite element method based onsingular+smoothstress field splitting
• A posteriorierror estimation for extended finite elements by an extended global recovery
• Some A Posteriori Error Estimators for Elliptic Partial Differential Equations
• Error Estimate Procedure in the Finite Element Method and Applications
• A simple error estimator and adaptive procedure for practical engineerng analysis
• 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
• Elastic crack growth in finite elements with minimal remeshing
• Special Finite Element Methods for a Class of Second Order Elliptic Problems with Rough Coefficients
• THE PARTITION OF UNITY METHOD
• Korn's inequalities for piecewise $H^1$ vector fields
• A proof of the trace theorem of Sobolev spaces on Lipschitz domains
• A finite element method for crack growth without remeshing
• A posteriori error analysis for Poisson's equation approximated by XFEM
• A simple error estimator for extended finite elements
• Zur Plattenberechnung mittels finiter Elemente
• Averaging technique for FE -- a posteriori error control in elasticity. I: Conforming FEM
• Corner singularities and regularity of weak solutions for the two-dimensional Lamé equations on domains with angular corners

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