Volume 5, Issue 2
A Posteriori Error Estimates of a Combined Mixed Finite Element and Discontinuous Galerkin Method for a Kind of Compressible Miscible Displacement Problems

Jiming Yang & Zhiguang Xiong

Adv. Appl. Math. Mech., 5 (2013), pp. 163-179.

Published online: 2013-05

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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

A posteriori error discontinuous Galerkin method compressible miscible displacement mixed finite element duality argument

  • AMS Subject Headings

65M12 65M60

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COPYRIGHT: © Global Science Press

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@Article{AAMM-5-163, author = {Jiming Yang and Zhiguang Xiong}, title = {A Posteriori Error Estimates of a Combined Mixed Finite Element and Discontinuous Galerkin Method for a Kind of Compressible Miscible Displacement Problems}, journal = {Advances in Applied Mathematics and Mechanics}, year = {2013}, volume = {5}, number = {2}, pages = {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.

}, issn = {2075-1354}, doi = {https://doi.org/10.4208/aamm.11-m1140}, url = {http://global-sci.org/intro/article_detail/aamm/63.html} }
TY - JOUR T1 - A Posteriori Error Estimates of a Combined Mixed Finite Element and Discontinuous Galerkin Method for a Kind of Compressible Miscible Displacement Problems AU - Jiming Yang & Zhiguang Xiong JO - Advances in Applied Mathematics and Mechanics VL - 2 SP - 163 EP - 179 PY - 2013 DA - 2013/05 SN - 5 DO - http://dor.org/10.4208/aamm.11-m1140 UR - https://global-sci.org/intro/article_detail/aamm/63.html KW - A posteriori error KW - discontinuous Galerkin method KW - compressible miscible displacement KW - mixed finite element KW - duality argument AB -

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.

Jiming Yang & Zhiguang Xiong. (1970). A Posteriori Error Estimates of a Combined Mixed Finite Element and Discontinuous Galerkin Method for a Kind of Compressible Miscible Displacement Problems. Advances in Applied Mathematics and Mechanics. 5 (2). 163-179. doi:10.4208/aamm.11-m1140
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