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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

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

Jiming Yang Email

Zhiguang Xiong Email

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  3. Error analysis of a two-grid discontinuous Galerkin method for non-linear parabolic equations

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    https://doi.org/10.1080/00207160.2014.988616 [Citations: 8]
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    Computational and Applied Mathematics, Vol. 42 (2023), Iss. 4

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    https://doi.org/10.1007/s11075-020-00943-4 [Citations: 7]