A combined stabilized mixed finite element and discontinuous Galerkin method for coupled Stokes and Darcy flows with transport

This paper presents a combined stabilized mixed finite element and discontinuous Galerkin method for coupled Stokes-Darcy flows model with transport, where the fluid viscosity depends on the concentration. We use nonconforming piecewise linear Crouzeix-Raviart (C-R) element to approximate velocity, piecewise constant function to approximate pressure and the symmetric interior penalty Galerkin (SIPG) method to solve concentration equation. A "cut-off" operator is introduced into SIPG scheme to avoid the assumption on the boundness of infinity norms of approximate velocity in convergence analysis. Optimal a priori error estimates for the full discrete scheme are obtained. Finally, some numerical examples are presented to verify the theoretical analysis, and a water injection oil production process is simulated to illustrate the practicability of our method.