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Superconvergence Analysis of a Full-Discrete Combined Mixed Finite Element and Discontinuous Galerkin Approximation for an Incompressible Miscible Displacement Problem

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Abstract

For an incompressible miscible displacement problem, an effective time-stepping procedure is proposed. The mixed finite element method is applied to the flow equation with uniform meshes, and the transport equation is solved by a full discretized interior penalty discontinuous Galerkin method with regular partitions. Convolution of the Darcy velocity approximation with the Bramble-Schatz kernel function and averaging are applied in the evaluation of the coefficients in the Galerkin procedure for the concentration. A superconvergence estimate is presented.

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Acknowledgements

This work was supported by Project funded by Project funded by China Postdoctoral Science Foundation (Grant No. 2014M562117), Scientific Research Fund of Hunan Provincial Education Department (Grant No. 14A034), the Planned Science and Technology Project of Hunan Province (Grant No. 2014FJ4258), Zhejiang Provincial Natural Science Foundation of China (Grant No. LQ13A010019), National Natural Science Foundation of China (Grant No. 11472103). The authors cordially thank the referees for their careful reading and helpful comments.

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Authors and Affiliations

  1. College of Science, Hunan Institute of Engineering, Xiangtan, 411104, Hunan, China

    Jiming Yang

  2. College of Civil Engineering and Mechanics, Xiangtan University, Xiangtan, 411105, Hunan, China

    Jiming Yang

  3. School of Mathematics and Computational Science, Hunan University of Science and Technology, Xiangtan, 411201, Hunan, China

    Zhiguang Xiong

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  1. Jiming Yang
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  2. Zhiguang Xiong
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Correspondence to Jiming Yang.

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Yang, J., Xiong, Z. Superconvergence Analysis of a Full-Discrete Combined Mixed Finite Element and Discontinuous Galerkin Approximation for an Incompressible Miscible Displacement Problem. Acta Appl Math 142, 107–121 (2016). https://doi.org/10.1007/s10440-015-0017-2

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  • DOI: https://doi.org/10.1007/s10440-015-0017-2

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