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Cut-Off Error Splitting Technique for Conservative Nonconforming VEM for N-Coupled Nonlinear Schrödinger–Boussinesq Equations

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Abstract

In this work, the error splitting technique combined with cut-off function method is designed to derive unconditionally optimal error estimates for a fully implicit conservative numerical method of the N-coupled nonlinear Schrödinger–Boussinesq equations, which is constructed by an implicit Crank–Nicolson-type method in time and new nonconforming virtual element methods in space. The numerical scheme is conservative in the senses of discrete mass and energy, and the cut-off error splitting technique is innovative to remove the standard time-step conditions \(\tau =o(h^{d/4})\) and \(\tau =o(h^{d/2})\). Finally, several numerical examples are given to confirm our theoretical results. The analytical technique in this work could be used to study other implicit numerical methods of nonlinear physical models, including but not limited to conforming and nonconforming finite element methods/virtual element methods.

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  1. School of Mathematics and Statistics, Zhengzhou University, Henan, 450001, China

    Meng Li

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This work was supported by NSF of China (Nos. 11801527), China Postdoctoral Science Foundation (Nos. 2018M632791).

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Li, M. Cut-Off Error Splitting Technique for Conservative Nonconforming VEM for N-Coupled Nonlinear Schrödinger–Boussinesq Equations. J Sci Comput 93, 86 (2022). https://doi.org/10.1007/s10915-022-02050-z

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