An optimal-order error estimate for a family of characteristic-mixedmethods to transient convection-diffusion problems

Huan-Zhen Chen; Zhao-Jie Zhou; Hong Wang; Hong-Ying Man

doi:10.3934/dcdsb.2011.15.325

Article Contents

2011, Volume 15, Issue 2: 325-341. Doi: 10.3934/dcdsb.2011.15.325

This issue Previous Article Preface Next Article Lyapunov stability for conservative systems with lower degrees of freedom

An optimal-order error estimate for a family of characteristic-mixed methods to transient convection-diffusion problems

1.
School of Mathematical Sciences, Shandong Normal University, Jinan 250014
2.
Department of Mathematics, University of South Carolina, Columbia, South Carolina 29208
3.
Department of Mathematics, Beijing Institute of Technology, Beijing 100081

Received: January 31, 2010

Revised: March 31, 2010

Published: August 2011

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Abstract

In this paper we prove an optimal-order error estimate for a family of characteristic mixed method with arbitrary degree of mixed finite element approximations for the numerical solution of transient convection diffusion equations. This paper generalizes the results in [1, 61]. The proof of the main results is carried out via three lemmas, which are utilized to overcome the difficulties arising from the combination of MMOC and mixed finite element methods. Numerical experiments are presented to justify the theoretical analysis.

Keywords:

Transient convection diffusion problems,
characteristic-mixed methods,
mixed finite element methods,
optimal order error estimate.

Mathematics Subject Classification: Primary: 65N30, 65N15; Secondary: 76M10.

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