Codice | 55/2016 |
Titolo | Discontinuous Galerkin approximation of flows in fractured porous media on polytopic grids |
Data | 2016-12-15 |
Autore/i | Antonietti, P. F.; Facciola' C.; Russo A.; Verani M.; |
Link | Download full text |
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 analyse 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. |
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