On the Robustness of Multiscale Hybrid-Mixed MethodsReport as inadecuate

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1 Instituto de Matematica - Pontificia Universidad Católica de Valparaíso - IMA - PUCV 2 Department of Computational and Applied Mathematics 3 UFRJ - Instituto de Matematica da Universidade Federal do Rio de Janeiro

Abstract : In this work we prove uniform convergence of the Multiscale Hybrid-Mixed MHM for short finite element method for second order elliptic problems with rough periodic coefficients. The MHM method is shown to avoid resonance errors without adopting oversampling techniques. In particular, we establish that the discretization error for the primal variable in the broken $H 1$ and $L $2 norms are $Oh + ε δ$ and $Oh 2 + h ε δ$, respectively, and for the dual variable is $Oh + ε δ$ in the $H$div; · norm, where $0 < δ ≤ 1-2$ depending on regularity. Such results rely on sharpened asymptotic expansion error estimates for the elliptic models with prescribed Dirichlet, Neumann or mixed boundary conditions.

Keywords : finite element hybridization multiscale method elliptic equation homogenization asymptotic expansion

Author: Diego Paredes - Frédéric Valentin - Henrique Versieux -

Source: https://hal.archives-ouvertes.fr/


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