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

被引：1
|
作者：
Yang, Huaijun [1 ]
机构：
[1] Zhengzhou Univ Aeronaut, Sch Math, Zhengzhou 450046, Henan, Peoples R China
来源：
COMMUNICATIONS ON APPLIED MATHEMATICS AND COMPUTATION | 2023年
基金：
中国国家自然科学基金;
关键词：
Unconditionally superconvergence error estimate; Nonlinear wave equation; Linearized energy-stable scalar auxiliary variable (SAV) Galerkin scheme; DIFFERENCE SCHEMES; CONVERGENCE; FEMS; APPROXIMATIONS;
D O I：
10.1007/s42967-023-00301-w
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
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 super-convergence 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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页数：18
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