Convergence and stability of the Lax-Friedrichs scheme for a nonlinear parabolic polymer flooding problem

Abstract

We prove convergence and stability of the Lax-Friedrichs scheme for a nonlinear parabolic system of partial differential equations. The system models a polymer flooding process in enhanced oil recovery. The properties of the approximate solutions are used to obtain existence, uniqueness, and stability results for the solution of the system. We illustrate by a numerical example that the solution of the parabolic system converges towards the solution of the corresponding hyperbolic system as the dispersion coefficient tends to zero. © 1990.