Mixed finite element methods for generalized forchheimer flow in porous media

Mixed finite element methods are analyzed for the approximation of the solution of the system of equations that describes the flow of a single-phase fluid in a porous medium in R-d, d less than or equal to 3, subject to Forchhheimer's law-a nonlinear form of Darcy's law. Existence and uniqueness of the approximation are proved, and optimal order error estimates in L-infinity(J; L-2(Omega)) and in Linfinity(J; H(div; Omega)) are demonstrated for the pressure and momentum, respectively. Error estimates are also derived in L-infinity(J; L-infinity(Omega)) for the pressure. (C) 2004 Wiley Periodicals. Inc.