Fully discrete mixed finite element approximations for non-Darcy flows in porous media

A numerical approximation procedure is proposed to solve equations describing non-Darcy flow of a single-phase fluid in a porous medium in two or three spacial dimensions, including the generalized Forchheimer equation. Fully discrete mixed finite element methods are considered and analyzed for the approximation. Existence and uniqueness of the approximation are discussed and optimal order error estimates in L² are derived for the three relevant functions.