Journal of Applied Mathematics
Volume 2011 (2011), Article ID 129724, 16 pages
doi:10.1155/2011/129724
Research Article

A Stabilized Mixed Finite Element Method for Single-Phase Compressible Flow

1School of Science, Xi'an Jiaotong University, Xi'an 710049, China
2Center for Computational Geosciences, Xi'an Jiaotong University, Xi'an 710049, China
3Department of Chemical and Petroleum Engineering, Schulich School of Engineering, University of Calgary, 2500 University Drive, NW Calgary, AB T2N 1N4, Canada

Received 6 December 2010; Accepted 2 January 2011

Academic Editor: Shuyu Sun

Copyright © 2011 Liyun Zhang and Zhangxin Chen. 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 present and study a stabilized mixed finite element method for single-phase compressible flow through porous media. This method is based on a pressure projection stabilization method for multiple-dimensional incompressible flow problems by using the lowest equal-order pair for velocity and pressure (i.e., the 𝐏 1 𝑃 1 pair). An optimal error estimate in divergence norm for the velocity and suboptimal error estimates in the 𝐿 2 -norm for both velocity and pressure are obtained. Numerical results are given in support of the developed theory.