Journal of Applied Mathematics
Volume 2011 (2011), Article ID 129724, 16 pages
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.
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 pair). An optimal error estimate in divergence norm for the velocity and suboptimal error estimates
in the -norm for both velocity and pressure are obtained. Numerical
results are given in support of the developed theory.