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\(L^p\) Error Estimates of Two-Grid Method for Miscible Displacement Problem

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Abstract

This paper is concerned about the \(L^p\) error analysis of two-grid method for incompressible miscible displacement in porous medium. A characteristics finite element method is presented for the concentration equation to handle the convection part, and standard mixed finite element is used for the pressure equation. Mixed finite element method has an advantage of approximating the unknown variable and its diffusive flux across grid-cell interfaces simultaneously, which has been proven to be an effective numerical method for solving fluid problems. Moreover, we linearize the equations based on the Newton iteration method, then, two-grid algorithm is considered in this full discrete scheme problems. It shown that coarse space can be extremely coarse and we achieve asymptotically optimal approximation. Numerical experiments are presented finally to validate the theoretical analysis.

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Authors and Affiliations

  1. School of Mathematical science, South China Normal University, Guangzhou, 520631, Guangdong, People’s Republic of China

    Yanping Chen & Jiaoyan Zeng

  2. School of Mathematical science, Xiangtan University, Xiangtan, 411105, Hunan, People’s Republic of China

    Jie Zhou

Authors
  1. Yanping Chen
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  2. Jiaoyan Zeng
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  3. Jie Zhou
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Correspondence to Yanping Chen.

Additional information

This work is supported by National Science Foundation of China (91430104, 11271145).

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Chen, Y., Zeng, J. & Zhou, J. \(L^p\) Error Estimates of Two-Grid Method for Miscible Displacement Problem. J Sci Comput 69, 28–51 (2016). https://doi.org/10.1007/s10915-016-0187-8

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  • DOI: https://doi.org/10.1007/s10915-016-0187-8

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