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Numerical analysis of a SUSHI scheme for an elliptic-parabolic system modeling miscible fluid flows in porous media

In this paper, we prove the convergence of a schema using stabilisation and hybrid interfaces of partial differential equations describing miscible displacement in porous media. This system is made of two coupled equations:an anisotropic diffusion equation on the pressure and a convection-diffusion dispersion equation on the concentration of invading fluid. The anisotropicdiffusion operators in both equations require special care while discretizing bya finite volume method SUSHI. Later, we present some numerical experiments.