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A Posteriori Error Estimates of a Combined Mixed Finite Element and Discontinuous Galerkin Method for a Kind of Compressible Miscible Displacement Problems

Published online by Cambridge University Press:  03 June 2015

Jiming Yang  and
Zhiguang Xiong
Jiming Yang*
Affiliation:
College of Science, Hunan Institute of Engineering, Xiangtan 411104, Hunan, China
Zhiguang Xiong*
Affiliation:
School of Mathematics and Computational Science, Hunan University of Science and Technology, Xiangtan 411201, Hunan, China
*
Corresponding author. Email: yangjiminghnie@163.com
Email: xiongzg2003@yahoo.com.cn
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Abstract

A kind of compressible miscible displacement problems which include molecular diffusion and dispersion in porous media are investigated. The mixed finite element method is applied to the flow equation, and the transport one is solved by the symmetric interior penalty discontinuous Galerkin method. Based on a duality argument, employing projection estimates and approximation properties, a posteriori residual-type hp error estimates for the coupled system are presented, which is often used for guiding adaptivity. Comparing with the error analysis carried out by Yang (Int. J. Numer. Meth. Fluids, 65(7) (2011), pp. 781–797), the current work is more complicated and challenging.

Keywords

65M1265M60A posteriori errordiscontinuous Galerkin methodcompressible miscible displacementmixed finite elementduality argument
Type
Research Article
Information
Advances in Applied Mathematics and Mechanics , Volume 5 , Issue 2 , April 2013 , pp. 163 - 179
Copyright
Copyright © Global-Science Press 2013

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