A mortar finite volume method for a fractured model in porous media

Abstract

In this paper, we consider a mortar finite volume method for a fractured model of flow in porous media. In this model, the permeability coefficients are variable between the fracture and the surrounding porous media. A finite volume method based on Raviart–Thomas elements combined with the mortar technique of domain decomposition is presented, in which sub-domains are triangulated independently and the meshes do not match at interfaces. The great advantage of the method is avoiding solving the saddle-point problem, since the numerical scheme is just related to the pressure p, and the velocity u can be expressed by p. We also prove error estimates of order h on the discrete H1 norm between the exact solution p and the mortar finite volume solution P and the (L2)2 norm between u and U. Finally, numerical experiments have been performed to show the consistency of the convergence rates with the theoretical analysis.