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A two-grid method for discontinuous Galerkin approximations to nonlinear Sobolev equations

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Abstract

A two-grid algorithm for discontinuous Galerkin approximations to nonlinear Sobolev equations is proposed. H1 norm error estimate of the two-grid method for the nonlinear parabolic problem is derived. The analysis shows that our two-grid discontinuous Galerkin algorithm will achieve asymptotically optimal approximation as long as the mesh sizes satisfy \(h = O(H^{\frac {r+1}{r}})\), where r is the order of the discontinuous finite element space. The numerical experiments are presented to prove the efficiency of our algorithm.

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Funding

This work was supported by Hunan Provincial Natural Science Foundation of China (Grant No. 2020JJ4242, 2019JJ50105).

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Authors and Affiliations

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

    Jiming Yang

  2. College of Textile and Garment, 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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Correspondence to Jiming Yang.

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Yang, J., Zhou, J. A two-grid method for discontinuous Galerkin approximations to nonlinear Sobolev equations. Numer Algor 86, 1523–1541 (2021). https://doi.org/10.1007/s11075-020-00943-4

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  • DOI: https://doi.org/10.1007/s11075-020-00943-4

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