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Unconditionally Superconvergence Error Analysis of an Energy-Stable and Linearized Galerkin Finite Element Method for Nonlinear Wave Equations

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Abstract

In this paper, a linearized energy-stable scalar auxiliary variable (SAV) Galerkin scheme is investigated for a two-dimensional nonlinear wave equation and the unconditional superconvergence error estimates are obtained without any certain time-step restrictions. The key to the analysis is to derive the boundedness of the numerical solution in the \(H^1\)-norm, which is different from the temporal-spatial error splitting approach used in the previous literature. Meanwhile, numerical results are provided to confirm the theoretical findings.

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The data that support the findings of this study are available from the corresponding author upon reasonable request.

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Acknowledgements

This work is supported by the National Natural Science Foundation of China (No. 12101568).

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  1. School of Mathematics, Zhengzhou University of Aeronautics, Zhengzhou, 450046, Henan, China

    Huaijun Yang

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  1. Huaijun Yang
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Yang, H. Unconditionally Superconvergence Error Analysis of an Energy-Stable and Linearized Galerkin Finite Element Method for Nonlinear Wave Equations. Commun. Appl. Math. Comput. (2023). https://doi.org/10.1007/s42967-023-00301-w

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  • DOI: https://doi.org/10.1007/s42967-023-00301-w

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