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

Resumo

A posteriori error estimation for multiscale hybrid-mixed formulations for Darcy’s problems is dis-
cussed. 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 po-
tential 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.