Computation of Quasi-Local Effective Diffusion Tensors and Connections to the Mathematical Theory of Homogenization

DOI10.1137/16M1088533zbMath1397.74185arXiv1608.02092OpenAlexW2623463482MaRDI QIDQ4601603

Daniel Peterseim, Dietmar Gallistl

Publication date: 17 January 2018

Published in: Multiscale Modeling & Simulation (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1608.02092

zbMATH Keywords

multiscale methoda posteriori error estimatesa priori error estimatesupscalingnumerical homogenization

Mathematics Subject Classification ID

Finite element methods applied to problems in solid mechanics (74S05) Error bounds for boundary value problems involving PDEs (65N15) Stability and convergence of numerical methods for boundary value problems involving PDEs (65N12) Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs (65N30) Homogenization in equilibrium problems of solid mechanics (74Q05)

Related Items (16)

Numerical homogenization beyond scale separation ⋮ An offline-online strategy for multiscale problems with random defects ⋮ Neural Network Approximation of Coarse-Scale Surrogates in Numerical Homogenization ⋮ Non-intrusive implementation of multiscale finite element methods: an illustrative example ⋮ An Elliptic Local Problem with Exponential Decay of the Resonance Error for Numerical Homogenization ⋮ Numerical multiscale methods for waves in high-contrast media ⋮ Computation of Quasi-Local Effective Diffusion Tensors and Connections to the Mathematical Theory of Homogenization ⋮ Reconstruction of quasi-local numerical effective models from low-resolution measurements ⋮ Sparse Compression of Expected Solution Operators ⋮ A generalized finite element method for problems with sign-changing coefficients ⋮ Efficient implementation of the localized orthogonal decomposition method ⋮ Numerical Homogenization of Elliptic PDEs with Similar Coefficients ⋮ Multiscale modeling, homogenization and nonlocal effects: Mathematical and computational issues ⋮ An analysis of the NLMC upscaling method for high contrast problems ⋮ A Priori Error Analysis of a Numerical Stochastic Homogenization Method ⋮ A Multiscale Method for Heterogeneous Bulk-Surface Coupling

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