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Discrete Dynamics in Nature and Society
Volume 2013 (2013), Article ID 264025, 9 pages
http://dx.doi.org/10.1155/2013/264025
Research Article

Quasi-Linear Convection-Dominated Transport Problem Based on Characteristics-Mixed Finite Element Method

1School of Management, Shandong University, Jinan, Shandong 250100, China
2Department of Mathematics, Beijing Institute of Technology, Beijing 100081, China

Received 3 July 2013; Accepted 4 August 2013

Academic Editor: Shurong Sun

Copyright © 2013 Peixin Zhao and Hongying Man. 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

We propose the characteristics-mixed method for approximating the solution to a convection-dominated transport problem. The new method is a combination of characteristic approximation to handle the convection part in time and a mixed finite element spatial approximation to deal with the diffusion part. Boundary conditions are incorporated in a natural fashion. The scheme is locally conservative since fluid is transported along the approximate characteristics on the discrete level and the test function can be piecewise constant. Analysis shows that the scheme has much smaller time-truncation errors than those of standard methods.