Unconditional error analysis of Galerkin FEMs for nonlinear fractional Schrödinger equation

Abstract

In this paper, we propose a conservative linearized Crank–Nicolson Galerkin FEMs for the nonlinear fractional Schrödinger 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 -norm error estimates are derived by the boundedness of the fully-discrete numerical solution in -norm. Finally, some numerical examples are given to confirm the theoretical results.

Keywords:

• Nonlinear fractional Schrödinger equation
• linearized Crank–Nicolson FEMs
• conservation
• unconditional convergence

Notes

No potential conflict of interest was reported by the authors.

Additional information

Funding

This work was supported by NSF of China [grant number 11371157] and Natural Science Foundation of Anhui Higher Education Institutions of China [grant number KJ2016A492].