  In this paper, we consider the generalized Forchheimer flows for slightly
compressible fluids in porous media. Using Muskat's and Ward's general form of
Forchheimer equations, we describe the flow of a single-phase fluid in $\mathbb
R^d, d\ge 2$ by a nonlinear degenerate 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. The continuous dependence of numerical solutions on
physical parameters are demonstrated. Experimental studies are presented
regarding convergence rates and showing the dependence of the solution on the
physical parameters.
