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Volume 41, Issue 2
Unconditionally Optimal Error Analysis of the Second-Order BDF Finite Element Method for the Kuramoto-Tsuzuki Equation

Yuan Li & Xuewei Cui

DOI: 10.4208/jcm.2107-m2020-0243

J. Comp. Math., 41 (2023), pp. 211-223.

Published online: 2022-11

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  • Abstract

This paper aims to study a second-order semi-implicit BDF finite element scheme for the Kuramoto-Tsuzuki equations in two dimensional and three dimensional spaces. The proposed scheme is stable and the nonlinear term is linearized by the extrapolation technique. Moreover, we prove that the error estimate in $L^2$-norm is unconditionally optimal which means that there has not any restriction on the time step and the mesh size. Finally, numerical results are displayed to illustrate our theoretical analysis.

  • Keywords

Kuramoto-Tsuzuki equations, BDF scheme, Finite element method, Optimal error analysis.

  • AMS Subject Headings

65N12, 65N15, 65N30

  • Copyright

COPYRIGHT: © Global Science Press

  • Email address

liyuan@wzu.edu.cn (Yuan Li)

cxwmath@163.com (Xuewei Cui)

  • BibTex
  • RIS
  • TXT
@Article{JCM-41-211, author = {Li , Yuan and Cui , Xuewei}, title = {Unconditionally Optimal Error Analysis of the Second-Order BDF Finite Element Method for the Kuramoto-Tsuzuki Equation}, journal = {Journal of Computational Mathematics}, year = {2022}, volume = {41}, number = {2}, pages = {211--223}, abstract = {

This paper aims to study a second-order semi-implicit BDF finite element scheme for the Kuramoto-Tsuzuki equations in two dimensional and three dimensional spaces. The proposed scheme is stable and the nonlinear term is linearized by the extrapolation technique. Moreover, we prove that the error estimate in $L^2$-norm is unconditionally optimal which means that there has not any restriction on the time step and the mesh size. Finally, numerical results are displayed to illustrate our theoretical analysis.

}, issn = {1991-7139}, doi = {https://doi.org/10.4208/jcm.2107-m2020-0243}, url = {http://global-sci.org/intro/article_detail/jcm/21177.html} }
TY - JOUR T1 - Unconditionally Optimal Error Analysis of the Second-Order BDF Finite Element Method for the Kuramoto-Tsuzuki Equation AU - Li , Yuan AU - Cui , Xuewei JO - Journal of Computational Mathematics VL - 2 SP - 211 EP - 223 PY - 2022 DA - 2022/11 SN - 41 DO - http://doi.org/10.4208/jcm.2107-m2020-0243 UR - https://global-sci.org/intro/article_detail/jcm/21177.html KW - Kuramoto-Tsuzuki equations, BDF scheme, Finite element method, Optimal error analysis. AB -

This paper aims to study a second-order semi-implicit BDF finite element scheme for the Kuramoto-Tsuzuki equations in two dimensional and three dimensional spaces. The proposed scheme is stable and the nonlinear term is linearized by the extrapolation technique. Moreover, we prove that the error estimate in $L^2$-norm is unconditionally optimal which means that there has not any restriction on the time step and the mesh size. Finally, numerical results are displayed to illustrate our theoretical analysis.

Li , Yuan and Cui , Xuewei. (2022). Unconditionally Optimal Error Analysis of the Second-Order BDF Finite Element Method for the Kuramoto-Tsuzuki Equation. Journal of Computational Mathematics. 41 (2). 211-223. doi:10.4208/jcm.2107-m2020-0243
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