A Mixed Finite Element Approximation of pre-Darcy Flows

Abstract

In this paper, we consider the pre-Darcy flows for slightly compressible fluids. Using Muskat's and Ward's general form of Forchheimer equations, we describe the fluid dynamics by a nonlinear system of density and momentum. A mixed finite element method is proposed for the approximation of the solution of the above system. The stability of the approximations are proved; the error estimates are derived for the numerical approximations for both continuous and discrete time procedures. Numerical experiments confirm the theoretical analysis regarding convergence rates.