A mixed and discontinuous Galerkin finite volume element method for incompressible miscible displacement problems in porous media

The incompressible miscible displacement problem in porous media is modeled by a coupled system of two nonlinear partial differential equations, the pressure-velocity equation and the concentration equation. In this article, we present a mixed finite volume element method for the approximation of pressure-velocity equation and a discontinuous Galerkin finite volume element method for the concentration equation. A priori error estimates in L∞(L2) are derived for velocity, pressure, and concentration. Numerical results are presented to substantiate the validity of the theoretical results. © 2011 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2012

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