An analytical framework for numerical homogenization - Part II: windowing and oversampling

Antoine Gloria 1
1 MICMAC - Methods and engineering of multiscale computing from atom to continuum
Inria Paris-Rocquencourt, ENPC - École des Ponts ParisTech
Abstract : In a recent paper (Multiscale Model. Simul., 5 (2006), No. 3, pp.~996-1043), the author has introduced an analytical framework to study the convergence properties of some numerical homogenization methods for elliptic problems. In the applications however, these methods are coupled with oversampling techniques. In the present work, the author addresses this issue within the latter framework and proves the convergence of the methods with oversampling, for convex and quasiconvex energies, in the context of general heterogeneities. This analysis provides us with an interesting variational interpretation of the Petrov-Galerkin formulation of the nonconforming multiscale finite element method for periodic problems.
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Multiscale Modeling and Simulation: A SIAM Interdisciplinary Journal, Society for Industrial and Applied Mathematics, 2008, 7 (1), pp.274-293. 〈10.1137/070683143〉
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Antoine Gloria. An analytical framework for numerical homogenization - Part II: windowing and oversampling. Multiscale Modeling and Simulation: A SIAM Interdisciplinary Journal, Society for Industrial and Applied Mathematics, 2008, 7 (1), pp.274-293. 〈10.1137/070683143〉. 〈inria-00132118v4〉

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