Unconditional error analysis of Galerkin FEMs for nonlinear fractional Schrodinger equation

作者：Li, Meng^*; Huang, Chengming; Zhang, Zongbiao

来源：APPLICABLE ANALYSIS, 2018, 97(2): 295-315.

DOI：10.1080/00036811.2016.1262947

• Nonlinear fractional Schrodinger equation
• linearized Crank-Nicolson FEMs
• conservation
• unconditional convergence

In this paper, we propose a conservative linearized Crank-Nicolson Galerkin FEMs for the nonlinear fractional Schrodinger equation. We construct5 a time-discrete system, to which, the mass conservation, semi-discrete error estimates and the suitable regularity of the numerical solution are obtained. With the spatial direction discreted by FEMs, the fully discrete conservative linearized finite element scheme is presented. Moreover, by a new error splitting technique, an unconditional L-2-norm error estimates are derived by the boundedness of the fully-discrete numerical solution in L-infinity-norm. Finally, some numerical examples are given to confirm the theoretical results.

• 出版日期2018
• 单位华中科技大学