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.

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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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