Electronic Journal of Differential Equations,
Conference 02 (1999), pp. 29-46.

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

Authors: Zhangxin Chen (Southern Methodist Univ., Dallas, TX, USA)
 Natalia L. Khlopina (Southern Methodist Univ., Dallas, TX, USA)
 
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 \cite{RckA} we analyzed the regularized
differential system and presented numerical results.  In the second paper
\cite{RckB} 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 December 9, 1999.
Math Subject Classifications: 35K60, 35K65, 76S05, 76T05.
Key Words:  porous medium; degenerate elliptic-parabolic system;
perturbation method; finite element; regularization; two-phase flow.