Journal
SIAM JOURNAL ON SCIENTIFIC COMPUTING
Volume 41, Issue 1, Pages A109-A138Publisher
SIAM PUBLICATIONS
DOI: 10.1137/17M1138194
Keywords
discontinuous Galerkin; polytopic grids; flows in fractured porous media
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Funding
- SIR Project - MIUR [RBSI14VT0S]
- Italian research grant [Prin 2012 2012HBLYE4]
- INdAM-GNCS
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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.
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