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A Stabilized Finite Element Method for Non-Stationary Conduction-Convection Problems

Published online by Cambridge University Press:  03 June 2015

Ke Zhao ,
Yinnian He  and
Tong Zhang
Ke Zhao*
Affiliation:
Faculty of Science, Xi’an Jiaotong University, Xi’an 710049, Shanxi, China
Yinnian He*
Affiliation:
Faculty of Science, Xi’an Jiaotong University, Xi’an 710049, Shanxi, China
Tong Zhang*
Affiliation:
School of Mathematics & Information Science, Henan Polytechnic University, Jiaozuo 454003, Henan, China
*
Email: mathszk@163.com
Corresponding author. URL: http://gr.xjtu.edu.cn:8080/web/heyn Email: heyn@mail.xjtu.edu.cn
Email: zhangtong0616@163.com
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Abstract

This paper is concerned with a stabilized finite element method based on two local Gauss integrations for the two-dimensional non-stationary conduction-convection equations by using the lowest equal-order pairs of finite elements. This method only offsets the discrete pressure space by the residual of the simple and symmetry term at element level in order to circumvent the inf-sup condition. The stability of the discrete scheme is derived under some regularity assumptions. Optimal error estimates are obtained by applying the standard Galerkin techniques. Finally, the numerical illustrations agree completely with the theoretical expectations.

Keywords

65N3065N1265Z05Non-stationary conduction-convection equationsfinite element methodstabilized methodstability analysiserror estimate
Type
Research Article
Information
Advances in Applied Mathematics and Mechanics , Volume 3 , Issue 2 , April 2011 , pp. 239 - 258
Copyright
Copyright © Global-Science Press 2011

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