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A two-gird method for finite element solution of parabolic integro-differential equations

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Abstract

In this paper, we study the unconditional convergence and error estimates of a two-grid finite element method for the semilinear parabolic integro-differential equations. By using a temporal-spatial error splitting technique, optimal \(L^p\) and \(H^1\) error estimates of the finite element method can be obtained. Moreover, to deal with the semilinearity of the model, we use the two-grid method. Optimal error estimates in \(L^2\) and \(H^1\)-norms of two-grid solution are derived without any time-step size conditions. Finally, some numerical results are provided to confirm the theoretical analysis, and show the efficiency of the proposed method.

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Authors and Affiliations

  1. School of Mathematics and Statistics, Hengyang Normal University, Hengyang, 421008, Hunan, People’s Republic of China

    Keyan Wang

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  1. Keyan Wang
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Correspondence to Keyan Wang.

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This work is supported by the Science and Technology Plan Project of Hunan Province (Grant No. 2016TP1020), the “Double First-Class” Applied Characteristic Discipline in Hunan Province(Xiangjiaotong[2018]469) and the Opening Project of Guangdong Province Key Laboratory of Computational Science at the Sun Yat-sen University (Grant No. 2021015)

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Wang, K. A two-gird method for finite element solution of parabolic integro-differential equations. J. Appl. Math. Comput. 68, 3473–3490 (2022). https://doi.org/10.1007/s12190-021-01670-2

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  • DOI: https://doi.org/10.1007/s12190-021-01670-2

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