Unconditionally Optimal Error Analysis of the Second-Order BDF Finite Element Method for the Kuramoto-Tsuzuki Equation
Year: 2023
Author: Yuan Li, Xuewei Cui
Journal of Computational Mathematics, Vol. 41 (2023), Iss. 2 : pp. 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.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/jcm.2107-m2020-0243
Journal of Computational Mathematics, Vol. 41 (2023), Iss. 2 : pp. 211–223
Published online: 2023-01
AMS Subject Headings:
Copyright: COPYRIGHT: © Global Science Press
Pages: 13
Keywords: Kuramoto-Tsuzuki equations BDF scheme Finite element method Optimal error analysis.
Author Details
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Unconditionally optimal error estimate of the Crank–Nicolson extrapolation Galerkin finite element method for Kuramoto–Tsuzuki equation
Yang, Huaijun
Computational and Applied Mathematics, Vol. 42 (2023), Iss. 6
https://doi.org/10.1007/s40314-023-02397-5 [Citations: 1]