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.