Unconditional stability and optimal error estimates of a Crank-Nicolson Legendre-Galerkin method for the two-dimensional second-order wave equation

Wenjie Liu; Boying Wu

doi:10.1007/s11075-021-01182-x

Unconditional stability and optimal error estimates of a Crank-Nicolson Legendre-Galerkin method for the two-dimensional second-order wave equation

Wenjie Liu
, Boying Wu^*

^*Corresponding author for this work

School of Mathematics

Research output: Contribution to journal › Article › peer-review

Abstract

This paper presents a fully discrete scheme by discretizing the space with the Legendre-Galerkin method and the time with the Crank-Nicolson method to solve the two-dimensional second-order wave equation. Unconditional stability and optimal error estimates in both L² and H¹ norms of the fully discrete Crank-Nicolson Galerkin method are obtained. Numerical results confirm exponential convergence of the proposed method in space and second-order convergence in time. Also, the numerical experiments show the discrete energy conservation and efficiency of long-time numerical calculation.

Original language	English
Pages (from-to)	137-158
Number of pages	22
Journal	Numerical Algorithms
Volume	90
Issue number	1
DOIs	https://doi.org/10.1007/s11075-021-01182-x
State	Published - May 2022

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Keywords

Crank-Nicolson Legendre-Galerkin method
Energy conservation
Second-order wave equation
Unconditional stability optimal error estimates

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10.1007/s11075-021-01182-x

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title = "Unconditional stability and optimal error estimates of a Crank-Nicolson Legendre-Galerkin method for the two-dimensional second-order wave equation",

abstract = "This paper presents a fully discrete scheme by discretizing the space with the Legendre-Galerkin method and the time with the Crank-Nicolson method to solve the two-dimensional second-order wave equation. Unconditional stability and optimal error estimates in both L2 and H1 norms of the fully discrete Crank-Nicolson Galerkin method are obtained. Numerical results confirm exponential convergence of the proposed method in space and second-order convergence in time. Also, the numerical experiments show the discrete energy conservation and efficiency of long-time numerical calculation.",

keywords = "Crank-Nicolson Legendre-Galerkin method, Energy conservation, Second-order wave equation, Unconditional stability optimal error estimates",

author = "Wenjie Liu and Boying Wu",

note = "Publisher Copyright: {\textcopyright} 2021, The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature.",

year = "2022",

month = may,

doi = "10.1007/s11075-021-01182-x",

language = "英语",

volume = "90",

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journal = "Numerical Algorithms",

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T1 - Unconditional stability and optimal error estimates of a Crank-Nicolson Legendre-Galerkin method for the two-dimensional second-order wave equation

AU - Liu, Wenjie

AU - Wu, Boying

PY - 2022/5

Y1 - 2022/5

N2 - This paper presents a fully discrete scheme by discretizing the space with the Legendre-Galerkin method and the time with the Crank-Nicolson method to solve the two-dimensional second-order wave equation. Unconditional stability and optimal error estimates in both L2 and H1 norms of the fully discrete Crank-Nicolson Galerkin method are obtained. Numerical results confirm exponential convergence of the proposed method in space and second-order convergence in time. Also, the numerical experiments show the discrete energy conservation and efficiency of long-time numerical calculation.

AB - This paper presents a fully discrete scheme by discretizing the space with the Legendre-Galerkin method and the time with the Crank-Nicolson method to solve the two-dimensional second-order wave equation. Unconditional stability and optimal error estimates in both L2 and H1 norms of the fully discrete Crank-Nicolson Galerkin method are obtained. Numerical results confirm exponential convergence of the proposed method in space and second-order convergence in time. Also, the numerical experiments show the discrete energy conservation and efficiency of long-time numerical calculation.

KW - Crank-Nicolson Legendre-Galerkin method

KW - Energy conservation

KW - Second-order wave equation

KW - Unconditional stability optimal error estimates

UR - https://www.scopus.com/pages/publications/85113757660

U2 - 10.1007/s11075-021-01182-x

DO - 10.1007/s11075-021-01182-x

M3 - 文章

AN - SCOPUS:85113757660

SN - 1017-1398

VL - 90

SP - 137

EP - 158

JO - Numerical Algorithms

JF - Numerical Algorithms

IS - 1

ER -

Unconditional stability and optimal error estimates of a Crank-Nicolson Legendre-Galerkin method for the two-dimensional second-order wave equation

Abstract

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Keywords

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