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Unconditional superconvergence analysis of an energy-stable L1 scheme for coupled nonlinear time-fractional prey-predator equations with nonconforming finite element

Author

Listed:
  • Shi, Dongyang
  • Zhang, Sihui

Abstract

The constrained nonconforming rotated Q1 (CNQ1rot) finite element is applied to develop an energy-stable L1 fully-discrete scheme through the Caputo fractional derivative approximation for the coupled nonlinear time-fractional prey-predator equations, and the unconditional superconvergence behavior is investigated. In which a novel high-accuracy estimate for the CNQ1rot element is given with the help of the Bramble-Hilbert (B-H) lemma, and the energy stability of the numerical solution is confirmed. Both of them are critical for demonstrating the unique solvability of the proposed scheme via the Brouwer fixed point theorem, and deducing the superclose estimation without any limitations between the spatial division size h and the time step τ. In addition, the above high-accuracy estimate can be extended to anisotropic meshes. Then, the unconditional superconvergence result is obtained by introducing the interpolation post-processing operator. Lastly, the theoretical findings are supported by some numerical experiments.

Suggested Citation

  • Shi, Dongyang & Zhang, Sihui, 2024. "Unconditional superconvergence analysis of an energy-stable L1 scheme for coupled nonlinear time-fractional prey-predator equations with nonconforming finite element," Applied Mathematics and Computation, Elsevier, vol. 467(C).
    • Handle: RePEc:eee:apmaco:v:467:y:2024:i:c:s009630032300663x
    DOI: 10.1016/j.amc.2023.128494
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    References listed on IDEAS

    as
    1. Lifang Pei & Dongyang Shi, 2013. "Superconvergence of a New Nonconforming Mixed Finite Element Scheme for Elliptic Problem," Mathematical Problems in Engineering, Hindawi, vol. 2013, pages 1-9, July.
    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. Shi, Dongyang & Zhang, Sihui, 2023. "Unconditional superconvergence analysis for the nonlinear Bi-flux diffusion equation," Applied Mathematics and Computation, Elsevier, vol. 442(C).
    4. Owolabi, Kolade M. & Karaagac, Berat, 2020. "Chaotic and spatiotemporal oscillations in fractional reaction-diffusion system," Chaos, Solitons & Fractals, Elsevier, vol. 141(C).
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    More about this item

    Keywords

    Coupled time-fractional prey-predator equations; CNQ1rot element and B-H lemma; Energy stability; L1 fully-discrete scheme; Unconditional superconvergence;
    All these keywords.

    JEL classification:

    • L1 - Industrial Organization - - Market Structure, Firm Strategy, and Market Performance

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