Error estimations for multiscale hybrid-mixed finite element methods for Darcy’s problems on polyhedral meshes

by Denise de Siqueira, Gustavo A. Batistela, Paulo R. Bösing, Phillippe R. B. Devloo, Sônia M. Gomes, presented at XLI Ibero-Latin American Congress on Computational Methods in Engineering, November 2020


A posteriori error estimation for multiscale hybrid-mixed formulations for Darcy’s problems is discussed. The method adopts two-scale finite element spaces: refined discretizations are adopted inside polygonal subregions, but flux approximations are constrained over the mesh interfaces by a given coarse normal trace space. For stability, pressure and flux approximations are divergence compatible. The error estimation is based on potential reconstruction, which is a popular technique for this kind of analysis in the context of mixed methods. Numerical experiments are presented in order to illustrate the efficiency of the proposals.