On the Robustness of multiscale hybrid-mixed methods
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