Discontinuous Galerkin approximation of flows in fractured porous media
Tuesday 24th May 2016
Antonietti, P.F.; Facciola', C.; Russo, A.;Verani, M.
We present a numerical approximation of Darcy's flow through a fractured porous medium which employs discontinuous Galerkin methods. For simplicity, we consider the case of a single fracture represented by a (d-1)-dimensional interface between two d-dimensional subdomains, d = 2; 3. We propose a discontinuous Galerkin Finite element approximation for the flow in the porous matrix which is coupled with a conforming finite element scheme for the flow in the fracture. Suitable (physically consistent) coupling conditions complete the model. We theoretically analyse the resulting formulation and prove its well-posedness. Moreover, we derive optimal a priori error estimates in a suitable (mesh-dependent) energy norm and we present two-dimensional numerical experiments assessing their validity.