Copyright © 2012 Tongjun Sun and Keying Ma. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

An approximation scheme is defined for incompressible miscible displacement in porous media. This scheme is constructed by two methods. Under the regularity assumption for the pressure, cubic Hermite finite element method is used for the pressure equation, which ensures the approximation of the velocity smooth enough. A second order characteristic finite element method is presented to handle the material derivative term of the concentration equation. It is of second order accuracy in time increment, symmetric, and unconditionally stable. The optimal -norm error estimates are derived for the scalar concentration.