Numerical solution of two-dimensional nonlinear Schrodinger equation using a new two-grid finite element method

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS

卷:364

Article

Hu, Hanzhang²  Chen, Yanping¹ 

[1] South China Normal Univ, Sch Math Sci, Guangzhou 510631, Guangdong, Peoples R China

[2] Jiaying Univ, Sch Math, Meizhou 514015, Guangdong, Peoples R China

关键词: Schrodinger equation;    Two-grid method;    Conservative;    Convergence;    Finite element method;   

DOI  :  10.1016/j.cam.2019.06.049

来源: Elsevier

【 摘 要 】

A new two-grid finite element scheme is presented for two-dimensional nonlinear Schrodinger equation. One Newton iteration is applied on the fine grid to linearize the nonlinear system using the coarse-grid solution as the initial guess, and furthermore one more linear system on the coarse space is solved. The error estimations of the two-grid solution in the L-2 and H-1 norm are given. It is shown, both theoretically and numerically, that the coarse space can be extremely coarse and two-grid aliorithm still achieves optimal approximation as long as the mesh sizes satisfy H = O(h(1/3)). (C) 2019 Elsevier B.V. All rights reserved.

【 授权许可】

Free