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

doi:10.1007/s42967-023-00301-w

Communications on Applied Mathematics and Computation ›› 2025, Vol. 7 ›› Issue (4): 1264-1281.doi: 10.1007/s42967-023-00301-w

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

Huaijun Yang

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

收稿日期:2023-03-21 修回日期:2023-07-06 接受日期:2023-07-27 出版日期:2023-09-15 发布日期:2023-09-15
通讯作者: Huaijun Yang,E-mail:huaijunyang@zua.edu.cn E-mail:huaijunyang@zua.edu.cn
基金资助:
This work is supported by the National Natural Science Foundation of China (No. 12101568).

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

Huaijun Yang

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

Received:2023-03-21 Revised:2023-07-06 Accepted:2023-07-27 Online:2023-09-15 Published:2023-09-15
Supported by:
This work is supported by the National Natural Science Foundation of China (No. 12101568).

摘要/Abstract

摘要： 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 H¹-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.

关键词: Unconditionally superconvergence error estimate, Nonlinear wave equation, Linearized energy-stable scalar auxiliary variable (SAV) Galerkin scheme

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 H¹-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.

Key words: Unconditionally superconvergence error estimate, Nonlinear wave equation, Linearized energy-stable scalar auxiliary variable (SAV) Galerkin scheme

中图分类号:

Huaijun Yang. Unconditionally Superconvergence Error Analysis of an Energy-Stable and Linearized Galerkin Finite Element Method for Nonlinear Wave Equations[J]. Communications on Applied Mathematics and Computation, 2025, 7(4): 1264-1281.

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

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

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