Mixed finite element methods for generalized Forchheimer flow in porous media - Park, Eun-Jae (Numerical methods for partial differential equations, 2005)
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 ℝd, d ≤ 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∞(J; L2(Ω)) and in L∞(J; H(div; Ω)) are demonstrated for the pressure and momentum, respectively. Error estimates are also derived in L∞(J; L∞(Ω)) for the pressure. © 2004 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2005