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Discontinuous Galerkin Time Stepping for Semilinear Parabolic Problems with Time Constant Delay

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Abstract

In this paper, a discontinuous Galerkin (DG) time stepping method combined with the standard finite element method in space is proposed to solve a class of semilinear parabolic differential equations with time constant delay. The time semi-discretization and the relevant global convergence of the DG solution under suitable uniform meshes are derived. The standard Galerkin method in space is used to obtain the fully discrete scheme and the optimal global convergence of the full discretization is presented. Numerical experiments for one-dimensional and two-dimensional equations are provided to demonstrate the theoretical results.

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Acknowledgements

The first author was supported by Anhui Natural Science Foundation (No. K120131028). The second author was supported by the National Natural Science Foundation of China (No. 11971047) and Beijing Natural Science Foundation (No. Z200002).

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Authors and Affiliations

  1. School of Mathematical Science, Anhui University, Hefei, 230601, China

    Xiuxiu Xu

  2. School of Mathematics, Faculty of Science, Beijing University of Technology, Beijing, 100124, China

    Qiumei Huang

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  1. Xiuxiu Xu
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Xu, X., Huang, Q. Discontinuous Galerkin Time Stepping for Semilinear Parabolic Problems with Time Constant Delay. J Sci Comput 96, 57 (2023). https://doi.org/10.1007/s10915-023-02278-3

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  • DOI: https://doi.org/10.1007/s10915-023-02278-3

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