Verification of stochastic models in uncertain environments using the constitutive relation error method

DOI10.1016/j.cma.2006.03.006zbMath1120.74820OpenAlexW1976200775MaRDI QIDQ2459225

Pierre Ladevèze, Eric Florentin

Publication date: 5 November 2007

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.2006.03.006

zbMATH Keywords

Finite element methodstochastic modelsA posteriori error estimationerrors in quantities of interest

Mathematics Subject Classification ID

Classical linear elasticity (74B05) Finite element methods applied to problems in solid mechanics (74S05) Random structure in solid mechanics (74E35)

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Cites Work

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• New advances on a posteriori error on constitutive relation in f. e. analysis
• A feed-back approach to error control in finite element methods: Application to linear elasticity
• A multigrid solver for two-dimensional stochastic diffusion equations.
• Local error estimators for finite element linear analysis
• On goal-oriented error estimation for elliptic problems: Application to the control of pointwise errors
• A posteriori estimation of the error in the error estimate
• Evaluation of the local quality of stresses in 3D finite element analysis.
• Finite elements for stochastic media problems
• Ingredients for a general purpose stochastic finite elements implementation
• 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
• Local error estimates of FEM for displacements and stresses in linear elasticity by solving local Neumann problems
• Sparse Quadrature as an Alternative to Monte Carlo for Stochastic Finite Element Techniques
• Error Estimate Procedure in the Finite Element Method and Applications
• A simple error estimator and adaptive procedure for practical engineerng analysis
• A‐posteriori error estimates for the finite element method
• A posteriori estimation and adaptive control of the pollution error in the h‐version of the finite element method
• Approximations in elasticity based on the concept of function space
• The generalized finite element method
• Monte Carlo strategies in scientific computing
• Solution of stochastic partial differential equations using Galerkin finite element techniques