A Posteriori Error Estimates of a Combined Mixed Finite Element and Discontinuous Galerkin Method for a Kind of Compressible Miscible Displacement Problems
Year: 2013
Author: Jiming Yang, Zhiguang Xiong
Advances in Applied Mathematics and Mechanics, Vol. 5 (2013), Iss. 2 : pp. 163–179
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.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/aamm.11-m1140
Advances in Applied Mathematics and Mechanics, Vol. 5 (2013), Iss. 2 : pp. 163–179
Published online: 2013-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 17
Keywords: A posteriori error discontinuous Galerkin method compressible miscible displacement mixed finite element duality argument.
Author Details
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