Name
Abstract | ||
|---|---|---|
Summary. This is the third paper of a series in which we analyze mathematical properties and develop numerical methods for a degenerate
elliptic-parabolic partial differential system which describes the flow of two incompressible, immiscible fluids in porous
media. In this paper we consider a finite element approximation for this system. The elliptic equation for the pressure and
velocity is approximated by a mixed finite element method, while the degenerate parabolic equation for the saturation is approximated
by a Galerkin finite element method. A fully discrete approximation is analyzed. Sharp error estimates in energy norms are
obtained for this approximation. The error analysis does not use any regularization of the saturation equation; the error
estimates are derived directly from the degenerate equation. Also, the analysis does not impose any restriction on the nature
of degeneracy. Finally, it respects the minimal regularity on the solution of the differential system.
|
Year | DOI | Venue |
|---|---|---|
2001 | 10.1007/s002110100291 | Numerische Mathematik |
Keywords | Field | DocType |
elliptic equation,porous media,incompressible flow,finite element method,numerical method,mixed finite element method | Degenerate energy levels,Mathematical analysis,Degeneracy (mathematics),Finite element method,Incompressible flow,Numerical analysis,Partial differential equation,Crank–Nicolson method,Mathematics,Mixed finite element method | Journal |
Volume | Issue | ISSN |
90 | 2 | 0945-3245 |
Citations | PageRank | References |
9 | 2.01 | 2 |
Authors | ||
2 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Zhang-Xin Chen | 1 | 347 | 67.13 |
| Richard E. Ewing | 2 | 252 | 45.87 |