We present a mathematical model of flow and solid mechanics in saturated fractured porous media based on the Biot poroelasticity. The fractures are treated as lower-dimensional manifolds on which the system of equations is projected onto the tangent space and coupled to the surrounding through interface conditions. The model can describe porous fractures, fractures filled only by a liquid and a transition between these two states.
Several finite-element and discontinuous-Galerkin discretizations are introduced and their stability is studied on a model problem. We decouple the system of equations to the flow and mechanics part and to the fracture and the surrounding domain. The convergence of iterative splittings for the decoupled problem is compared to the monolithic approach.
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