A posteriori error analysis of the heterogeneous multiscale method for homogenization problems

DOI10.1016/j.crma.2009.07.004zbMath1172.65060OpenAlexW2089757800MaRDI QIDQ841299

Achim Nonnenmacher, Assyr Abdulle

Publication date: 15 September 2009

Published in: Comptes Rendus. Mathématique. Académie des Sciences, Paris (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.crma.2009.07.004

zbMATH Keywords

finite element methodadaptive mesh refinementmultiscale methoda posteriori error estimateselliptic homogenization problems

Mathematics Subject Classification ID

Boundary value problems for second-order elliptic equations (35J25) Error bounds for boundary value problems involving PDEs (65N15) Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs (65N30) Mesh generation, refinement, and adaptive methods for boundary value problems involving PDEs (65N50) Homogenization in context of PDEs; PDEs in media with periodic structure (35B27)

Related Items (14)

Estimates of the modeling error generated by homogenization of an elliptic boundary value problem ⋮ A posteriori error estimation and adaptivity in non-intrusive couplings between concurrent models ⋮ An Introductory Review on A Posteriori Error Estimation in Finite Element Computations ⋮ Reduced basis finite element heterogeneous multiscale method for high-order discretizations of elliptic homogenization problems ⋮ Discontinuous Galerkin finite element heterogeneous multiscale method for elliptic problems with multiple scales ⋮ Adaptive finite element heterogeneous multiscale method for homogenization problems ⋮ Error control and adaptivity for heterogeneous multiscale approximations of nonlinear monotone problems ⋮ \textit{A posteriori} error estimation and adaptive strategy for the control of MsFEM computations ⋮ Goal-oriented error estimation and adaptivity in MsFEM computations ⋮ A stochastic mixed finite element heterogeneous multiscale method for flow in porous media ⋮ A goal-oriented error estimator for a class of homogenization problems ⋮ A-posteriori error estimate for a heterogeneous multiscale approximation of advection-diffusion problems with large expected drift ⋮ An Adaptive Multiscale Finite Element Method ⋮ A posteriori error estimates in quantities of interest for the finite element heterogeneous multiscale method

Uses Software

• AFEM@matlab

Cites Work

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• A Framework for Adaptive Multiscale Methods for Elliptic Problems
• Heterogeneous Multiscale FEM for Diffusion Problems on Rough Surfaces
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• ANALYSIS OF A HETEROGENEOUS MULTISCALE FEM FOR PROBLEMS IN ELASTICITY
• A Posteriori Error Estimates for the Heterogeneous Multiscale Finite Element Method for Elliptic Homogenization Problems
• On A Priori Error Analysis of Fully Discrete Heterogeneous Multiscale FEM

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