Goal-oriented explicit residual-type error estimates in XFEM

DOI10.1007/s00466-012-0816-5zbMath1398.74397OpenAlexW2075779035MaRDI QIDQ356839

Erwin Stein, Tymofiy Gerasimov, Marcus Olavi Rüter

Publication date: 26 July 2013

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

Full work available at URL: https://doi.org/10.1007/s00466-012-0816-5

zbMATH Keywords

dualityFEMXFEMexplicit residual-type error estimationgoal-oriented a posteriori error estimationLEFM

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)

Related Items (8)

Goal functional evaluations for phase-field fracture using PU-based DWR mesh adaptivity ⋮ Constant-free explicit error estimator with sharp upper error bound property for adaptive FE analysis in elasticity and fracture ⋮ Subdomain-based error techniques for generalized finite element approximations of problems with singular stress fields ⋮ An adaptive scaled boundary finite element method for contact analysis ⋮ A hierarchically enhanced recovery-based error estimator for bidimensional elastoplastic modelling by generalized finite element approach ⋮ Quantifying discretization errors for soft tissue simulation in computer assisted surgery: a preliminary study ⋮ A recovery-explicit error estimator in energy norm for linear elasticity ⋮ Error-controlled adaptive extended finite element method for 3D linear elastic crack propagation

Cites Work

• Unnamed Item
• Unnamed Item
• Accurate recovery-based upper error bounds for the extended finite element framework
• The superconvergent patch recovery (SPR) and adaptive finite element refinement
• On the duality of finite element discretization error control in computational Newtonian and Eshelbian mechanics
• 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
• Goal-oriented a posteriori error estimates in linear elastic fracture mechanics
• Corrected Stabilized Non-conforming Nodal Integration in Meshfree Methods
• An explicit residual-type error estimator for Q1-quadrilateral extended finite element method in two-dimensional linear elastic fracture mechanics
• Recent Developments and Innovative Applications in Computational Mechanics
• 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
• 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
• A simple error estimator and adaptive procedure for practical engineerng analysis
• A‐posteriori error estimates for the finite element method
• Error Estimates for Adaptive Finite Element Computations
• Elastic crack growth in finite elements with minimal remeshing
• Crack propagation in continuous media
• A finite element method for crack growth without remeshing
• VI. The phenomena of rupture and flow in solids
• The force on an elastic singularity
• Corner singularities and regularity of weak solutions for the two-dimensional Lamé equations on domains with angular corners

This page was built for publication: Goal-oriented explicit residual-type error estimates in XFEM