Combined mixed finite element and nonconforming finite volume methods for flow and transport in porous media

This paper is concerned with numerical methods for a coupled system of two partial differential equations (PDEs), modeling flow and transport of a contaminant in porous media. This coupled system, arising in modeling of flow and transport in heterogeneous porous media, includes two types of equations: an elliptic and a diffusion-convection equation. We focus on miscible flow in heterogeneous porous media. We use the mixed finite element method for the Darcy flow equation over triangles, and for the concentration equation, we use nonconforming finite volume methods in unstructured mesh. Finally, we show the existence and uniqueness of a solution of this coupled scheme and demonstrate the effectiveness of the methodology by a series of numerical examples.