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Section: New Results

Stochastic homogenization

A. Gloria has followed up on a work by X. Blanc, C. Le Bris (EPI MICMAC) and P.-L. Lions on a variant of stochastic homogenization. In particular, he has proved in [21] that for such a random structure a subadditive ergodic theorem still holds, which allows to generalize the homogenization results to the case of multiple integrals (and in particular nonlinear elasticity). Further results are the object of a collaboration with F. Otto (U. of Bonn, Germany) which started during A. Gloria's post-doc, and an article is currently in preparation. Moreover, A. Gloria has continued his study of numerical homogenization of elliptic PDEs, analyzing in [20] the method of windowing and oversampling used by practitioners (both in solid mechanics and flow in porous media).


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