Superconvergence of a full‐discrete combined mixed finite element and discontinuous Galerkin method for a compressible miscible displacement problem |
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| Authors: | Jiming Yang Yanping Chen Zhiguang Xiong |
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| Institution: | 1. College of Science, Hunan Institute of Engineering, Xiangtan 411104, People's Republic of China;2. School of Mathematical Sciences, South China Normal University, Guangzhou 510631, People's Republic of China;3. School of Mathematics and Computational Science, Hunan University of Science and Technology, Xiangtan 411201, People's Republic of China |
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| Abstract: | An efficient time‐stepping procedure is investigated for a two‐dimensional compressible miscible displacement problem in porous media in which the mixed finite element method with Raviart‐Thomas space is applied to the flow equation, and the transport one is solved by the symmetric interior penalty discontinuous Galerkin approximation on Cartesian meshes. Based on the projection interpolations and the induction hypotheses, a superconvergence error estimate is obtained. During the analysis, an extension of the Darcy velocity along the Gauss line is also used in the evaluation of the coefficients in the Galerkin procedure for the concentration. © 2013 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2013 |
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| Keywords: | compressible discontinuous Galerkin method full‐discrete mixed finite element superconvergence |
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