International Journal of Mathematics and Mathematical Sciences
Volume 2012 (2012), Article ID 870402, 21 pages
Research Article

A Second Order Characteristic Method for Approximating Incompressible Miscible Displacement in Porous Media

School of Mathematics, Shandong University, Jinan 250100, China

Received 25 March 2012; Revised 5 July 2012; Accepted 28 July 2012

Academic Editor: Nistor Victor

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.


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 𝐿 2 -norm error estimates are derived for the scalar concentration.