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Structure-preserving BDF2 FE method for the coupled Schrödinger-Boussinesq equations

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Abstract

In this article, a structure-preserving second-order backward difference formula (BDF2) finite element (FE) method for finding the numerical solution of nonlinear coupled Schrödinger-Boussinesq equations (NCSBEs) is presented and discussed, where the space direction is approximated by Galerkin FE method and the time direction is discretized making use of the BDF2. The important thing is that the approximate conservation results of mass and energy with sufficiently small time step length τ are proved. The stability of the scheme and the optimal convergence results in L2-norm are derived in detail. Finally, numerical experiments are done to demonstrate the optimal theory results and conservation results.

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All data analyzed during this study are included in this article.

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Acknowledgements

The authors thank editors and reviewers very much for their valuable suggestions for improving our work.

Funding

This work is supported by the National Natural Science Foundation of China (12061053, 12161063), Natural Science Foundation of Inner Mongolia (2021MS01018), Young innovative talents project of Grassland Talents Project, Program for Innovative Research Team in Universities of Inner Mongolia Autonomous Region (NMGIRT2207), and National Innovation Project (202110126023).

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Authors and Affiliations

  1. School of Mathematical Sciences, Inner Mongolia University, Hohhot, 010021, China

    Yining Yang, Ziyu Sun, Yang Liu & Hong Li

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  1. Yining Yang
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  2. Ziyu Sun
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  3. Yang Liu
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  4. Hong Li
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Contributions

Y.N. Yang and Y. Liu wrote the main manuscript text, Z.Y. Sun implemented the numerical tests, and H. Li and Y. Liu checked the full text. All authors reviewed and approved the manuscript.

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Correspondence to Yang Liu.

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Yang, Y., Sun, Z., Liu, Y. et al. Structure-preserving BDF2 FE method for the coupled Schrödinger-Boussinesq equations. Numer Algor 93, 1243–1267 (2023). https://doi.org/10.1007/s11075-022-01466-w

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