We present a numerical approximation of Darcy's flow through a fractured porous medium which employs discontinuous Galerkin methods on polytopic grids. For simplicity, we analyze 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 analyze the resulting formulation, prove its well-posedness, and derive optimal a priori error estimates in a suitable (mesh-dependent) energy norm. Two-dimensional numerical experiments are reported to assess the theoretical results.
Antonietti, P., Facciola, C., Russo, A., Verani, M. (2019). Discontinuous Galerkin approximation of flows in fractured porous media on polytopic grids. SIAM JOURNAL ON SCIENTIFIC COMPUTING, 41(1), A109-A138 [10.1137/17M1138194].
Discontinuous Galerkin approximation of flows in fractured porous media on polytopic grids
Russo, A;
2019
Abstract
We present a numerical approximation of Darcy's flow through a fractured porous medium which employs discontinuous Galerkin methods on polytopic grids. For simplicity, we analyze 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 analyze the resulting formulation, prove its well-posedness, and derive optimal a priori error estimates in a suitable (mesh-dependent) energy norm. Two-dimensional numerical experiments are reported to assess the theoretical results.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.