Zhangxin Chen & Natalia L. Khlopina
This is the third paper of a three-part series where we develop and analyze a finite element approximation for a degenerate elliptic-parabolic partial differential system which describes the flow of two incompressible, immiscible fluids in porous media. The approximation uses a mixed finite element method for the pressure equation and a Galerkin finite element method for the saturation equation. It is based on a regularization of the saturation equation. In the first paper  we analyzed the regularized differential system and presented numerical results. In the second paper  we obtained error estimates. In the present paper we describe a perturbation analysis for the saturation equation and numerical experiments for complementing this analysis.
Published November 24, 1999.
Subject lassfications: 35K60, 35K65, 76S05, 76T05.
Key words: porous medium, degenerate elliptic-parabolic system, perturbation method, finite element, regularization, two-phase flow.
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Natalia L. Khlopina
Department of Mathematics
Box 750156, Southern Methodist University
Dallas, TX 75275-0156 USA