Codice | 22/2016 |
Titolo | Discontinuous Galerkin approximation of flows in fractured porous media |
Data | 2016-05-24 |
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. 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. |
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