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.
Bibliographical noteFunding Information:
*The research of this author was supported in part by a post-doctoral fellowship from the University of Trento, Italy. ?The research of this author was supported in part by G.N.A.F.A. of C.N.R. (Italy) and KOSEF #97070101013 (Korea).
All Science Journal Classification (ASJC) codes
- Modelling and Simulation
- Computational Theory and Mathematics
- Computational Mathematics