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A characteristic finite element two-grid algorithm for a compressible miscible displacement problem

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Abstract

A nonlinear parabolic system is derived to describe compressible miscible displacement in a porous medium. A mixed finite element method is employed to approximate the pressure and the Darcy velocity, and a characteristic finite element method is used to approximate the concentration. Twice Newton iteration is applied on the fine grid to linearize the fully discrete problem using the coarse-grid solution as the initial guess. Moreover, the Lq error estimates are conducted for the pressure, Darcy velocity, and concentration variables in the two-grid solutions. It is shown both theoretically and numerically that the coarse space can be extremely coarse, with no loss in the order of accuracy, and the two-grid algorithm still achieves the optimal approximation as long as the mesh sizes satisfy \(H = O(h^{\frac {1}{4}})\). The numerical results show that this algorithm is very effective.

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Funding

This work is financially supported by the National Natural Science Foundation of China (11671157, 11931003, 41974133, 11971410) and the Natural Science Foundation of Guangdong province, China (2018A0303100016).

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Authors and Affiliations

  1. School of Mathematics, Jiaying University, Meizhou, 514015, Guangdong, People’s Republic of China

    Hanzhang Hu

  2. School of Mathematical Science, South China Normal University, Guangzhou, 510631, Guangdong, People’s Republic of China

    Yanping Chen

  3. Hunan Key Laboratory for Computation and Simulation in Science and Engineering, School of Mathematics and Computational Science, Xiangtan University, Xiangtan, 411105, Hunan, People’s Republic of China

    Yunqing Huang

Authors
  1. Hanzhang Hu
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  2. Yanping Chen
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  3. Yunqing Huang
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Correspondence to Yanping Chen.

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Communicated by: Ivan Graham

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Hu, H., Chen, Y. & Huang, Y. A characteristic finite element two-grid algorithm for a compressible miscible displacement problem. Adv Comput Math 46, 15 (2020). https://doi.org/10.1007/s10444-020-09768-0

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  • DOI: https://doi.org/10.1007/s10444-020-09768-0

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