Mathematical Problems in Engineering
Volume 2011 (2011), Article ID 370192, 28 pages
doi:10.1155/2011/370192
Research Article

A Defect-Correction Mixed Finite Element Method for Stationary Conduction-Convection Problems

Faculty of Science, Xi'an Jiaotong University, Xi'an 710049, China

Received 29 July 2010; Revised 15 November 2010; Accepted 5 January 2011

Academic Editor: Katica R. (Stevanovic) Hedrih

Copyright © 2011 Zhiyong Si and Yinnian He. 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

A defect-correction mixed finite element method (MFEM) for solving the stationary conduction-convection problems in two-dimension is given. In this method, we solve the nonlinear equations with an added artificial viscosity term on a grid and correct this solution on the same grid using a linearized defect-correction technique. The stability is given and the error analysis in 𝐿 2 and 𝐻 1 -norm of 𝑢 , 𝑇 and the 𝐿 2 -norm of 𝑝 are derived. The theory analysis shows that our method is stable and has a good precision. Some numerical results are also given, which show that the defect-correction MFEM is highly efficient for the stationary conduction-convection problems.