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Applicable Analysis
An International Journal
Volume 97, 2018 - Issue 2
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Original Articles

Unconditional error analysis of Galerkin FEMs for nonlinear fractional Schrödinger equation

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Pages 295-315 | Received 24 Jul 2016, Accepted 15 Nov 2016, Published online: 28 Nov 2016
 

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.

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].

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