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The nonlinear Forchheimer equations are used to describe the dynamics offluid flows in porous media when Darcy's law is not applicable. In thisarticle, we consider the generalized Forchheimer flows for slightlycompressible fluids, and then study the expanded mixed finite element methodapplied to the initial boundary value problem for the resulting degenerateparabolic equation for pressure. The bounds for the solutions, time derivativeand gradient of solutions are established. Utilizing the monotonicityproperties of Forchheimer equation and boundedness of solutions, a {\it priori} error estimates for solution are obtained in $L^2$-norm, $L^\infty$-norm aswell as for its gradient in $L^{2-a}$-norm for all $a\in (0,1)$. Optimal$L^2$-error estimates are shown for solutions under some additional regularityassumptions. Numerical results using the lowest order Raviart-Thomas mixedelement confirm the theoretical analysis regarding convergence rates.

Analysis of expanded mixed finite element methods for the generalized Forchheimer equations