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Two-grid methods of finite element solutions for semi-linear elliptic interface problems

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Abstract

In this paper, we present two efficient two-grid algorithms for solving two-dimensional semi-linear elliptic interface problems using finite element method. To linearize the finite element equations, the Newton iteration approach and correction technique are applied. The new two-grid schemes reduce the solution of the semi-linear interface problem on a fine grid to one linear interface equation on the same fine grid and an original interface problem on a much coarser grid. Therefore, the new schemes save total computational cost. Theoretical analysis shows that the two-grid methods maintain asymptotically optimal accuracy, and the numerical experiments presented confirm the theoretical results.

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Funding

This work is supported by National Science Foundation of China (11671157, 11826212) and Hunan Provincial Innovation Foundation for Postgraduate (CX2017B273).

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Authors and Affiliations

  1. School of Mathematical Sciences, South China Normal University, Guangzhou, People’s Republic of China

    Yanping Chen

  2. School of Mathematics and Computational Science, Xiangtan University, Xiangtan, Hunan, People’s Republic of China

    Qingfeng Li & Yang Wang

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

    Yunqing Huang

Authors
  1. Yanping Chen
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  2. Qingfeng Li
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  3. Yang Wang
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  4. Yunqing Huang
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Correspondence to Yanping Chen.

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Chen, Y., Li, Q., Wang, Y. et al. Two-grid methods of finite element solutions for semi-linear elliptic interface problems. Numer Algor 84, 307–330 (2020). https://doi.org/10.1007/s11075-019-00756-0

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