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 - <p style="text-align: justify;">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.</p>