Local error estimates of FEM for displacements and stresses in linear elasticity by solving local Neumann problems

DOI10.1002/nme.228zbMath1057.74042OpenAlexW2128497093MaRDI QIDQ2763357

Erwin Stein, Elmar Walhorn, Stephan Ohnimus

Publication date: 2001

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.228

zbMATH Keywords

explicit residual error estimationimplicit posterior equilibrium method

Mathematics Subject Classification ID

Classical linear elasticity (74B05) Finite element methods applied to problems in solid mechanics (74S05) Error bounds for boundary value problems involving PDEs (65N15)

Related Items

Error bounds for the reliability index in finite element reliability analysis, A non-intrusive method for the calculation of strict and efficient bounds of calculated outputs of interest in linear viscoelasticity problems, Pointwise Error Estimation for the One-Dimensional Transport Equation Based on the Variational Multiscale Method, Stress and flux reconstruction in Biot's poro-elasticity problem with application to a posteriori error analysis, Equilibrated stress tensor reconstruction and a posteriori error estimation for nonlinear elasticity, New bounding techniques for goal-oriented error estimation applied to linear problems, Constant-free explicit error estimator with sharp upper error bound property for adaptive FE analysis in elasticity and fracture, An Introductory Review on A Posteriori Error Estimation in Finite Element Computations, A posteriori error estimators for stabilized \(P\)1 nonconforming approximation of the Stokes problem, Implicit upper bound error estimates for combined expansive model and discretization adaptivity, A constitutive relation error estimator based on traction-free recovery of the equilibrated stress, An a posteriori error estimator for two-body contact problems on non-matching meshes, Verification of stochastic models in uncertain environments using the constitutive relation error method, Model adaptivity for finite element analysis of thin or thick plates based on equilibrated boundary stress resultants, Adaptive meshing for local quality of FE stresses, A posteriori error estimators for nonconforming finite element methods of the linear elasticity problem, Local estimation of the error in the von Mises' stress and L2‐norm of the stress for linear elasticity problems, A posteriori error estimator and error control for contact problems, Variational multiscale a posteriori error estimation for systems. Application to linear elasticity, A unified approach to strict upper and lower bounds of quantities in linear elasticity based on constitutive relation error estimation, Strict bounding of quantities of interest in computations based on domain decomposition, Study of the strong prolongation equation for the construction of statically admissible stress fields: implementation and optimization, A posteriori pointwise error computation for 2-D transport equations based on the variational multiscale method, Implicit a posteriori error estimation in cut finite elements, Anisotropic discretization- and model-error estimation in solid mechanics by local Neumann problems, Hierarchical models of thin elastic structures: overview and recent advances in error estimation and adaptivity, Error-controlled adaptive goal-oriented modeling and finite element approximations in elasticity, Goal-oriented a posteriori error estimates in linear elastic fracture mechanics

Cites Work

• Adaptive finite element methods in computational mechanics
• 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
• Coupled model- and solution-adaptivity in the finite element method
• A posteriori error estimation in finite element analysis
• Pollution error in the \(h\)-version of the finite element method and the local quality of the recovered derivatives
• A posteriori error estimation in large-strain elasticity using equilibrated local Neumann problems
• On goal-oriented error estimation for elliptic problems: Application to the control of pointwise errors
• Anisotropic discretization- and model-error estimation in solid mechanics by local Neumann problems
• A posteriori error estimation and adaptivity for linear elasticity using the reciprocal theorem
• Zur Plattenberechnung mittels finiter Elemente