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Unconditional optimal error estimates of a two-grid method for semilinear parabolic equation

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  • Shi, Dongyang
  • Yang, Huaijun

Abstract

In this paper, the error analysis of a two-grid method (TGM) with backward Euler scheme is discussed for semilinear parabolic equation. Contrary to the conventional finite element analysis, the error between exact solution and finite element solution is split into two parts (temporal error and spatial error) by introducing a corresponding time-discrete system. This can lead to the spatial error independent of τ (time step). Secondly, based on the above technique, optimal error estimates in L2 and H1-norms of TGM solution are deduced unconditionally, while previous works always require a certain time step size condition. Finally, a numerical experiment is provided to confirm the theoretical analysis.

Suggested Citation

  • Shi, Dongyang & Yang, Huaijun, 2017. "Unconditional optimal error estimates of a two-grid method for semilinear parabolic equation," Applied Mathematics and Computation, Elsevier, vol. 310(C), pages 40-47.
    • Handle: RePEc:eee:apmaco:v:310:y:2017:i:c:p:40-47
    DOI: 10.1016/j.amc.2017.04.010
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    References listed on IDEAS

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    1. Shi, Dongyang & Wang, Junjun, 2017. "Unconditional superconvergence analysis for nonlinear hyperbolic equation with nonconforming finite element," Applied Mathematics and Computation, Elsevier, vol. 305(C), pages 1-16.
    2. Zhu, Liping & Chen, Zhangxin, 2015. "A two-level stabilized nonconforming finite element method for the stationary Navier–Stokes equations," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 114(C), pages 37-48.
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    Citations

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    Cited by:

    1. Pei, Lifang & Zhang, Chaofeng & Shi, Dongyang, 2024. "Unconditional superconvergence analysis of two-grid nonconforming FEMs for the fourth order nonlinear extend Fisher-Kolmogorov equation," Applied Mathematics and Computation, Elsevier, vol. 471(C).
    2. Shi, Dongyang & Wu, Yanmi, 2020. "Uniformly superconvergent analysis of an efficient two-grid method for nonlinear Bi-wave singular perturbation problem," Applied Mathematics and Computation, Elsevier, vol. 367(C).
    3. Wu, Yanmi & Shi, Dongyang, 2021. "Quasi-uniform and unconditional superconvergence analysis of Ciarlet–Raviart scheme for the fourth order singularly perturbed Bi-wave problem modeling d-wave superconductors," Applied Mathematics and Computation, Elsevier, vol. 397(C).
    4. Li, Zhenzhen & Li, Minghao & Shi, Dongyang, 2021. "Unconditional convergence and superconvergence analysis for the transient Stokes equations with damping," Applied Mathematics and Computation, Elsevier, vol. 389(C).

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