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Abstract and Applied Analysis
Volume 2013 (2013), Article ID 580461, 10 pages
http://dx.doi.org/10.1155/2013/580461
Research Article

A Rectangular Mixed Finite Element Method with a Continuous Flux for an Elliptic Equation Modelling Darcy Flow

School of Mathematics, Shandong University, Jinan 250100, China

Received 26 March 2013; Accepted 29 May 2013

Academic Editor: Santanu Saha Ray

Copyright © 2013 Xindong Li and Hongxing Rui. 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 introduce a mixed finite element method for an elliptic equation modelling Darcy flow in porous media. We use a staggered mesh where the two components of the velocity and the pressure are defined on three different sets of grid nodes. In the present mixed finite element, the approximate velocity is continuous and the conservation law still holds locally. The LBB consistent condition is established, while the error estimates are obtained for both the velocity and the pressure. Numerical examples are presented to confirm the theoretical analysis.