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      Reduced-Basis approach for homogenization beyond the periodic setting

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          Abstract

          We consider the computation of averaged coefficients for the homogenization of elliptic partial differential equations. In this problem, like in many multiscale problems, a large number of similar computations parametrized by the macroscopic scale is required at the microscopic scale. This is a framework very much adapted to model order reduction attempts. The purpose of this work is to show how the reduced-basis approach allows to speed up the computation of a large number of cell problems without any loss of precision. The essential components of this reduced-basis approach are the {\it a posteriori} error estimation, which provides sharp error bounds for the outputs of interest, and an approximation process divided into offline and online stages, which decouples the generation of the approximation space and its use for Galerkin projections.

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          A Multiscale Finite Element Method for Numerical Homogenization

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            Generalized p-FEM in homogenization

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              Author and article information

              Journal
              2007-02-22
              Article
              math/0702674
              f3b8af97-0a36-4298-9939-128629c9af1c
              History
              Custom metadata
              math.NA
              ccsd inria-00132763

              Numerical & Computational mathematics
              Numerical & Computational mathematics

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