A coupled HDG/DG method for porous media with conducting/sealing faults

We introduce and analyze a coupled hybridizable discontinuous Galerkin/discontinuous Galerkin (HDG/DG) method for porous media in which we allow fully and partly immersed faults, and faults that separate the domain into two disjoint subdomains. We prove well-posedness and present an a priori error analysis of the discretization. Numerical examples verify our analysis.