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Unconditional superconvergence analysis for the nonlinear Bi-flux diffusion equation

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  • Shi, Dongyang
  • Zhang, Sihui

Abstract

The fourth-order Bi-flux diffusion equation with a nonlinear reaction term is studied by the linear finite element method (FEM). First, a novel important property of high accuracy of this element is proved by the Bramble-Hilbert (B-H) lemma, which is essential to the superconvergence analysis. Then, the Backward-Euler (B-E) and Crank-Nicolson (C-N) fully discrete schemes are developed, and the stabilities of their numerical solutions and the unique solvabilities are demonstrated. Furthermore, by applying a splitting argument to dealing with the nonlinear term, the superconvergence results in H1-norm are derived without any restriction between the mesh size h and the time step τ. Finally, numerical results are presented to verify the rationality of the theoretical analysis.

Suggested Citation

  • Shi, Dongyang & Zhang, Sihui, 2023. "Unconditional superconvergence analysis for the nonlinear Bi-flux diffusion equation," Applied Mathematics and Computation, Elsevier, vol. 442(C).
    • Handle: RePEc:eee:apmaco:v:442:y:2023:i:c:s0096300322008396
    DOI: 10.1016/j.amc.2022.127771
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    Cited by:

    1. 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).

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