On the Robustness of multiscale hybrid-mixed methods

Resumen

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 and  norms are   and , respectively, and for the dual variable it is   in the   norm, where  (depending on regularity). Such results rely on sharpened asymptotic expansion error estimates for the elliptic models with prescribed Dirichlet, Neumann or mixed boundary conditions.

Autores: Paredes, D., Valentin, F., Versieux, H.

Journal: Mathematics of Computation

Journal Volume: 86

Journal Issue: 304

Journal Page: 525-548

Tipo de publicación: ISI

Fecha de publicación: 2017

Topics: asymptotic expansion, homogenization, elliptic equation, multiscale method, hybridization, finite element

DOI: https://doi.org/10.1090/mcom/3108

URL de la publicación: http://www.ams.org/journals/mcom/2017-86-304/S0025-5718-2016-03108-7/S0025-5718-2016-03108-7.pdf