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.
引用
收藏
页数：18
相关论文
共 50 条
  • [31] Unconditionally energy-stable discontinuous Galerkin method for the chemo-repulsion-Navier-Stokes system
    Wang, Meiting
    Zou, Guang-an
    Wang, Bo
    Zhao, Wenju
    COMPUTERS & MATHEMATICS WITH APPLICATIONS, 2023, 150 : 132 - 155
  • [32] SUPERCONVERGENCE ERROR ESTIMATES OF THE LOWEST-ORDER RAVIART-THOMAS GALERKIN MIXED FINITE ELEMENT METHOD FOR NONLINEAR THERMISTOR EQUATIONS
    Yang, Huaijun
    Shi, Dongyang
    JOURNAL OF COMPUTATIONAL MATHEMATICS, 2024,
  • [33] Unconditional superconvergence analysis of an energy-stable L1 scheme for coupled nonlinear time-fractional prey-predator equations with nonconforming finite element
    Shi, Dongyang
    Zhang, Sihui
    APPLIED MATHEMATICS AND COMPUTATION, 2024, 467
  • [34] Superconvergence analysis of an H1-Galerkin mixed finite element method for Sobolev equations
    Shi, Dongyang
    Wang, Junjun
    COMPUTERS & MATHEMATICS WITH APPLICATIONS, 2016, 72 (06) : 1590 - 1602
  • [35] Numerical analysis of an unconditionally energy-stable reduced-order finite element method for the Allen-Cahn phase field model
    Li, Huanrong
    Wang, Dongmei
    Song, Zhengyuan
    Zhang, Fuchen
    Computers and Mathematics with Applications, 2021, 96 : 67 - 76
  • [36] Numerical analysis of an unconditionally energy-stable reduced-order finite element method for the Allen-Cahn phase field model
    Li, Huanrong
    Wang, Dongmei
    Song, Zhengyuan
    Zhang, Fuchen
    COMPUTERS & MATHEMATICS WITH APPLICATIONS, 2021, 96 : 67 - 76
  • [37] UNCONDITIONALLY SUPERCLOSE ANALYSIS OF A NEW MIXED FINITE ELEMENT METHOD FOR NONLINEAR PARABOLIC EQUATIONS
    Shi, Dongyang
    Yan, Fengna
    Wang, Junjun
    JOURNAL OF COMPUTATIONAL MATHEMATICS, 2019, 37 (01) : 1 - 17
  • [38] Superconvergence Analysis of Anisotropic Finite Element Method for a Kind of Nonlinear Degenerate Wave Equation
    Li, Zhiyan
    Liu, Linghui
    Qu, Jingguo
    Cui, Yuhuan
    INFORMATION COMPUTING AND APPLICATIONS, PT 2, 2010, 106 : 341 - +
  • [39] Unconditionally convergence and superconvergence error analysis of a mass- and energy-conserved finite element method for the Schrödinger-Poisson equation
    Yang, Huaijun
    Liu, Xia
    COMPUTATIONAL & APPLIED MATHEMATICS, 2024, 43 (05):
  • [40] Superconvergence analysis of an H1-Galerkin mixed finite element method for nonlinear BBM equation
    Shi, Xiangyu
    Lu, Linzhang
    APPLIED MATHEMATICS LETTERS, 2019, 90 : 146 - 153
12345