Unconditional superconvergence analysis for the nonlinear Bi-flux diffusion equation

Dongyang Shi and Sihui Zhang

Applied Mathematics and Computation, 2023, vol. 442, issue C

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.

Keywords: Bi-flux diffusion; Linear finite element; Stability and unique solvability; Splitting argument; Unconditional superconvergence (search for similar items in EconPapers)
Date: 2023
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Citations: View citations in EconPapers (1)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:442:y:2023:i:c:s0096300322008396

DOI: 10.1016/j.amc.2022.127771

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