Error-controlled adaptive goal-oriented modeling and finite element approximations in elasticity

DOI10.1016/j.cma.2006.10.032zbMath1173.74443OpenAlexW2084344232MaRDI QIDQ1033375

Stephan Ohnimus, Erwin Stein, Marcus Olavi Rüter

Publication date: 6 November 2009

Published in: Computer Methods in Applied Mechanics and Engineering (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.cma.2006.10.032

zbMATH Keywords

discretization errormodel errorgoal-oriented a posteriori error estimationprolongations

Mathematics Subject Classification ID

Classical linear elasticity (74B05) Nonlinear elasticity (74B20) Finite element methods applied to problems in solid mechanics (74S05)

Related Items (9)

Duality-based adaptive model reduction for one-way coupled thermoelastic problems ⋮ Constant-free explicit error estimator with sharp upper error bound property for adaptive FE analysis in elasticity and fracture ⋮ Coupled model and grid adaptivity in hierarchical reduction of elliptic problems ⋮ Adaptive hpq finite element methods for the analysis of 3D-based models of complex structures. I: Hierarchical modeling and approximations ⋮ Implicit upper bound error estimates for combined expansive model and discretization adaptivity ⋮ Goal-oriented \(r\)-adaptivity based on variational arguments in the physical and material spaces ⋮ Adjoint-based error estimation and mesh adaptation for stabilized finite deformation elasticity ⋮ Variational multiscale a posteriori error estimation for systems. Application to linear elasticity ⋮ A posteriori pointwise error computation for 2-D transport equations based on the variational multiscale method

Cites Work

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• Goal-oriented error estimates based on different FE-spaces for the primal and the dual problem with applications to fracture 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 unified approach to a posteriori error estimation using element residual methods
• Estimation of local modeling error and goal-oriented adaptive modeling of heterogeneous materials. I: Error estimates and adaptive algorithms
• 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
• The efficient computation of bounds for functionals of finite element solutions in large strain elasticity.
• Estimation of modeling error in computational mechanics.
• A posteriori estimation and adaptive control of the error in the quantity of interest. I: A posteriori estimation of the error in the von Mises stress and the stress intensity factor
• A posteriori error estimation and adaptivity for linear elasticity using the reciprocal theorem
• Goal-oriented a posteriori error estimates in linear elastic fracture mechanics
• Adaptive computational meso-macro-scale modeling of elastic composites
• Local error estimates of FEM for displacements and stresses in linear elasticity by solving local Neumann problems
• Adaptive finite element analysis and modelling of solids and structures. Findings, problems and trends
• 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
• An Adaptive Finite Element Method for Linear Elliptic Problems
• The superconvergent patch recovery anda posteriori error estimates. Part 1: The recovery technique
• A‐posteriori error estimates for the finite element method
• Zur Plattenberechnung mittels finiter Elemente
• Averaging technique for FE -- a posteriori error control in elasticity. I: Conforming FEM
• The generalized finite element method

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