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A Two-Grid Combined Mixed Finite Element and Discontinuous Galerkin Method for an Incompressible Miscible Displacement Problem in Porous Media

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Abstract

An incompressible miscible displacement problem is investigated. A two-grid algorithm of a full-discretized combined mixed finite element and discontinuous Galerkin approximation to the miscible displacement in porous media is proposed. The error estimate for the concentration in \(H^1\)-norm and the error estimates for the pressure and the velocity in \(L^2\)-norm are obtained. The analysis shows that the asymptotically optimal approximation can be achieved as long as the mesh size satisfies \(h = O(H^2)\), where H and h are the sizes of the coarse mesh and the fine mesh, respectively. Meanwhile, the effectiveness of the presented algorithm is verified by numerical experiments, from which it can be seen that the algorithm is spent much less time.

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Authors and Affiliations

  1. School of Computational Science and Electronics, Hunan Institute of Engineering, Xiangtan, 411104, Hunan, China

    Jiming Yang & Yifan Su

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  1. Jiming Yang
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  2. Yifan Su
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Correspondence to Jiming Yang.

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This work was supported by Project funded by Hunan Provincial Natural Science Foundation of China (Grant No. 2020JJ4242, 2019JJ50105), Scientific Research Fund of Hunan Provincial Education Department (Grant No. 18A351, 17C0393).

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Yang, J., Su, Y. A Two-Grid Combined Mixed Finite Element and Discontinuous Galerkin Method for an Incompressible Miscible Displacement Problem in Porous Media. J Sci Comput 88, 81 (2021). https://doi.org/10.1007/s10915-021-01596-8

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  • DOI: https://doi.org/10.1007/s10915-021-01596-8

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