Electronic Journal of Differential Equations 15th annual Conference of Applied Mathematics, Univ. of Central Oklahoma,
Electron. J. Diff. Eqns., Conf. 02, 1999, pp. 29-46.

Degenerate two-phase incompressible flow problems III: Perturbation analysis and numerical experiments

Zhangxin Chen & Natalia L. Khlopina

Abstract:
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 [15] we analyzed the regularized differential system and presented numerical results. In the second paper [16] 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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Zhangxin Chen
Department of Mathematics
Box 750156, Southern Methodist University
Dallas, TX 75275-0156 USA
e-mail: zchen@dragon.math.smu.edu

Natalia L. Khlopina
Department of Mathematics
Box 750156, Southern Methodist University
Dallas, TX 75275-0156 USA
e-mail: khlopina@mail.smu.edu


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