A Rectangular Mixed Finite Element Method with a Continuous Flux for an Elliptic Equation Modelling Darcy Flow

Abstract

We introduce a mixed finite element method for an elliptic equation modelling Darcy flow in porous media. We use a staggered mesh where the two components of the velocity and the pressure are defined on three different sets of grid nodes. In the present mixed finite element, the approximate velocity is continuous and the conservation law still holds locally. The LBB consistent condition is established, while the $L\mathrm{2}$ error estimates are obtained for both the velocity and the pressure. Numerical examples are presented to confirm the theoretical analysis.