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Advances in Numerical Analysis
Volume 2013 (2013), Article ID 303952, 13 pages
http://dx.doi.org/10.1155/2013/303952
Research Article

Parallel Nonoverlapping DDM Combined with the Characteristic Method for Incompressible Miscible Displacements in Porous Media

School of Mathematics, Shandong University, Jinan, Shandong 250100, China

Received 28 May 2012; Revised 27 October 2012; Accepted 1 November 2012

Academic Editor: J. Rappaz

Copyright © 2013 Keying Ma and Tongjun Sun. 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

Two types of approximation schemes are established for incompressible miscible displacements in porous media. First, standard mixed finite element method is used to approximate the velocity and pressure. And then parallel non-overlapping domain decomposition methods combined with the characteristics method are presented for the concentration. These methods use the characteristic method to handle the material derivative term of the concentration equation in the subdomains and explicit flux calculations on the interdomain boundaries by integral mean method or extrapolation method to predict the inner-boundary conditions. Thus, the velocity and pressure can be approximated simultaneously, and the parallelism can be achieved for the concentration equation. The explicit nature of the flux prediction induces a time step limitation that is necessary to preserve stability. These schemes hold the advantages of nonoverlapping domain decomposition methods and the characteristic method. Optimal error estimates in -norm are derived for these two schemes, respectively.