Mixed-primal Discontinuous Galerkin approximation of flows in fractured porous media on polygonal and polyhedral grids
Keywords
Advanced Numerical Methods for Scientific Computing
Code:
14/2019
Title:
Mixed-primal Discontinuous Galerkin approximation of flows in fractured porous media on polygonal and polyhedral grids
Date:
Friday 31st May 2019
Author(s):
Antonietti, P.F.; Facciolà, C; Verani, M.
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Abstract:
We propose a formulation based on discontinuous Galerkin methods on polygonal/polyhedral grids for the simulation of flows in fractured porous media. We adopt a model for single-phase flows where the fracture is modelled as a (d - 1) - dimensional interface in a d - dimensional bulk domain and the flow is governed by the Darcy's law
in both the bulk and the fracture. The two problems are then coupled through physically consistent conditions. We focus on the numerical approximation of the coupled bulk-fracture problem, discretizing the bulk problem in mixed form and the fracture problem in primal form. We present an priori h- and p-version error estimate in a suitable (mesh-dependent) energy norm and numerical tests assessing it.