Convergence Analysis for The Numerical Boundary Corrector for Elliptic Equations with Rapidly Oscillating Coefficients

DOI10.1137/060654773zbMath1176.65123OpenAlexW2132239270MaRDI QIDQ3624382

Henrique Versieux, Markus V. Sarkis

Publication date: 30 April 2009

Published in: SIAM Journal on Numerical Analysis (Search for Journal in Brave)

Full work available at URL: https://semanticscholar.org/paper/7b01e53d227019a814db57a07156051853496007

zbMATH Keywords

asymptotic expansiondiscontinuous coefficientshomogenizationboundary layercomposite materialsa priori error estimatesecond order elliptic equationperiodic equationmixed finite element scheme

Mathematics Subject Classification ID

Boundary value problems for second-order elliptic equations (35J25) Singular perturbations in context of PDEs (35B25) 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) PDEs with low regular coefficients and/or low regular data (35R05)

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L²-GLOBAL TO LOCAL PROJECTION: AN APPROACH TO MULTISCALE ANALYSIS ⋮ Asymptotic analysis of second-order boundary layer correctors ⋮ Interior Hölder and gradient estimates for the homogenization of the linear elliptic equations ⋮ On the robustness of multiscale hybrid-mixed methods ⋮ Error Estimate of Multiscale Finite Element Method for Periodic Media Revisited ⋮ Limiting boundary correctors for periodic microstructures and inverse homogenization series ⋮ Homogenization in polygonal domains ⋮ Numerical investigation of homogenized Stokes-Nernst-Planck-Poisson systems ⋮ Third-order corrections in periodic homogenization for elliptic problem ⋮ Hybrid Localized Spectral Decomposition for Multiscale Problems

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