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A linearized element-free Galerkin method for the complex Ginzburg–Landau equation
Computers & Mathematics with Applications ( IF 2.9 ) Pub Date : 2021-04-05 , DOI: 10.1016/j.camwa.2021.03.027
Xiaolin Li , Shuling Li

In this paper, an effective linearized element-free Galerkin (EFG) method is developed for the numerical solution of the complex Ginzburg–Landau (GL) equation. To deal with the time derivative and the nonlinear term of the GL equation, an explicit linearized procedure is presented. The unconditional stability and the error estimate of the procedure are analyzed. Then, a stabilized EFG method is proposed to establish linear algebraic systems. In the method, the penalty technique is used to facilitate the satisfaction of boundary conditions, and the stabilized moving least squares approximation is used to enhance the stability and performance. The linearized EFG method is a meshless method and possesses high precision and convergence rate in both space and time. Theoretical error and convergence of the linearized EFG method are analyzed. Finally, some numerical results are provided to demonstrate the efficiency of the method and confirm the theoretical results.



中文翻译:

复杂的Ginzburg–Landau方程的线性化无元素Galerkin方法

本文针对复杂的Ginzburg-Landau(GL)方程的数值解,开发了一种有效的线性化无元素Galerkin(EFG)方法。为了处理GL方程的时间导数和非线性项,提出了一个明确的线性化过程。分析了程序的无条件稳定性和误差估计。然后,提出了一种稳定的EFG方法来建立线性代数系统。在该方法中,使用惩罚技术来促进边界条件的满足,并且使用稳定的移动最小二乘近似来增强稳定性和性能。线性化EFG方法是一种无网格方法,在时空上均具有较高的精度和收敛速度。分析了线性EFG方法的理论误差和收敛性。最后,

更新日期:2021-04-05
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