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 V(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.
|Number of pages||16|
|Journal||Numerical Methods for Partial Differential Equations|
|Publication status||Published - 2005 Mar 1|
All Science Journal Classification (ASJC) codes
- Applied Mathematics
- Computational Mathematics