On the robustness of multiscale hybrid-mixed methods

Abstract

© 2016 American Mathematical Society. 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 H1 and L2 norms are O(h+εδ) and O(h2 +hεδ), respectively, and for the dual variable it is O(h+εδ) in the H(div;) norm, where 0