J. Comp. Math., 33 (2015), pp. 146-157. |
A Two-Grid Finite-Element Method for the Nonlinear Schrödinger Equation Jicheng Jin ^{1}, Ning Wei ^{2}, Hongmei Zhang ^{3} 1 School of Science, Hunan University of Technology, Zhuzhou 412007, Hunan, China2 School of Mathematics and Computational Science, Xiangtan University, Xiangtan 411105, Hunan, China 3 School of Science, Hunan University of Technology, Zhuzhou 412007, Hunan, China; School of Mathematics and Computational Science, Xiangtan University, Xiangtan 411105, Hunan, China Received 2012-11-29 Accepted 2014-9-1 Available online 2015-3-13 doi:10.4208/jcm.1409-m4323 Abstract In this paper, some two-grid finite element schemes are constructed for solving the nonlinear Schrödinger equation. With these schemes, the solution of the original problem is reduced to the solution of the same problem on a much coarser grid together with the solutions of two linear problems on a fine grid. We have shown, both theoretically and numerically, that our schemes are efficient and achieve asymptotically optimal accuracy. Key words: Nonlinear Schrödinger equation, Finite element method, Two-grid. AMS subject classifications: 65N30, 65N55. Email: jcjin2008@sina.com, weiningjiayou@126.com, zhm10180@yahoo.com.cn |