Reduced basis finite element heterogeneous multiscale method for quasilinear elliptic homogenization problems

DOI10.3934/dcdss.2015.8.91zbMath1304.65245OpenAlexW2126541999MaRDI QIDQ479073

Assyr Abdulle, Yun Bai, Gilles Vilmart

Publication date: 5 December 2014

Published in: Discrete and Continuous Dynamical Systems. Series S (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.3934/dcdss.2015.8.91

zbMATH Keywords

convergencefinite element methodgreedy algorithmNewton methodmultiscale methoda posteriori error estimatorreduced basis methodquasilinearnumerical experimentnumerical homogenizationnonlinear nonmonotone elliptic problems

Mathematics Subject Classification ID

Multigrid methods; domain decomposition for boundary value problems involving PDEs (65N55) 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) Nonlinear constitutive equations for materials with memory (74D10) Homogenization in context of PDEs; PDEs in media with periodic structure (35B27) Quasilinear elliptic equations (35J62)

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Uses Software

• rbMIT

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