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

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.

Keywords

• porous medium
• degenerate elliptic-parabolic system
• perturbation method
• finite element
• regularization
• two-phase flow.