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Volume 29, Issue 1
A Priori Error Estimates of a Combined Mixed Finite Element and Discontinuous Galerkin Method for Compressible Miscible Displacement with Molecular Diffusion and Dispersion

Jiming Yang & Yanping Chen

DOI: 10.4208/jcm.1006-m2991

J. Comp. Math., 29 (2011), pp. 91-107.

Published online: 2011-02

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  • Abstract

A combined approximation for a kind of compressible miscible displacement problems including molecular diffusion and dispersion in porous media is studied. Mixed finite element method is applied to the flow equation, and the transport one is solved by the symmetric interior penalty discontinuous Galerkin method (SIPG). To avoid the inconvenience of the cut-off operator in [3,21], some induction hypotheses different from the ones in [6] are used. Based on interpolation projection properties, a priori $hp$ error estimates are obtained. Comparing with the existing error analysis that only deals with the diffusion case, the current work is more complicated and more significant.

  • Keywords

A priori error, Mixed finite element, Discontinuous Galerkin, Compressible miscible displacement.

  • AMS Subject Headings

65M12, 65M60.

  • Copyright

COPYRIGHT: © Global Science Press

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  • TXT
@Article{JCM-29-91, author = {Jiming Yang and Yanping Chen}, title = {A Priori Error Estimates of a Combined Mixed Finite Element and Discontinuous Galerkin Method for Compressible Miscible Displacement with Molecular Diffusion and Dispersion}, journal = {Journal of Computational Mathematics}, year = {2011}, volume = {29}, number = {1}, pages = {91--107}, abstract = {

A combined approximation for a kind of compressible miscible displacement problems including molecular diffusion and dispersion in porous media is studied. Mixed finite element method is applied to the flow equation, and the transport one is solved by the symmetric interior penalty discontinuous Galerkin method (SIPG). To avoid the inconvenience of the cut-off operator in [3,21], some induction hypotheses different from the ones in [6] are used. Based on interpolation projection properties, a priori $hp$ error estimates are obtained. Comparing with the existing error analysis that only deals with the diffusion case, the current work is more complicated and more significant.

}, issn = {1991-7139}, doi = {https://doi.org/10.4208/jcm.1006-m2991}, url = {http://global-sci.org/intro/article_detail/jcm/8466.html} }
TY - JOUR T1 - A Priori Error Estimates of a Combined Mixed Finite Element and Discontinuous Galerkin Method for Compressible Miscible Displacement with Molecular Diffusion and Dispersion AU - Jiming Yang & Yanping Chen JO - Journal of Computational Mathematics VL - 1 SP - 91 EP - 107 PY - 2011 DA - 2011/02 SN - 29 DO - http://doi.org/10.4208/jcm.1006-m2991 UR - https://global-sci.org/intro/article_detail/jcm/8466.html KW - A priori error, Mixed finite element, Discontinuous Galerkin, Compressible miscible displacement. AB -

A combined approximation for a kind of compressible miscible displacement problems including molecular diffusion and dispersion in porous media is studied. Mixed finite element method is applied to the flow equation, and the transport one is solved by the symmetric interior penalty discontinuous Galerkin method (SIPG). To avoid the inconvenience of the cut-off operator in [3,21], some induction hypotheses different from the ones in [6] are used. Based on interpolation projection properties, a priori $hp$ error estimates are obtained. Comparing with the existing error analysis that only deals with the diffusion case, the current work is more complicated and more significant.

Jiming Yang and Yanping Chen. (2011). A Priori Error Estimates of a Combined Mixed Finite Element and Discontinuous Galerkin Method for Compressible Miscible Displacement with Molecular Diffusion and Dispersion. Journal of Computational Mathematics. 29 (1). 91-107. doi:10.4208/jcm.1006-m2991
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