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Analysis of a full-discrete two-grid discontinuous Galerkin method for nonlinear parabolic equations

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Abstract

A full-discrete two-grid discontinuous Galerkin approximation for nonlinear parabolic problems is proposed. The \(L^2\)-norm error analysis of the two-grid method is carried out. The analysis shows that our algorithm will achieve an asymptotically optimal approximation as long as mesh sizes satisfy \(h = O(H^2)\), where H and h are the size of the coarse mesh and the fine mesh, respectively. Numerical examples are presented to test the efficiency of our algorithm.

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Authors and Affiliations

  1. College of Science, Central South University of Forestry and Technology, Changsha, 410004, Hunan, China

    Jiming Yang, Jing Zhou & Hongbin Chen

  2. Institute of Higher Education Research, Hunan Institute of Engineering, Xiangtan, 411104, Hunan, China

    Jing Zhou

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  1. Jiming Yang
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  2. Jing Zhou
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  3. Hongbin Chen
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Correspondence to Jiming Yang.

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Communicated by Paul Cizmas.

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This work was supported by project funded by Natural Science Foundation of Hunan Province (Grant No. 2020JJ4242, 2022JJ30996), Scientific Research Fund of Hunan Provincial Education Department (Grant No. 21C0585, 20B139).

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Yang, J., Zhou, J. & Chen, H. Analysis of a full-discrete two-grid discontinuous Galerkin method for nonlinear parabolic equations. Comp. Appl. Math. 42, 149 (2023). https://doi.org/10.1007/s40314-023-02297-8

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  • DOI: https://doi.org/10.1007/s40314-023-02297-8

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