摘要
Abstract.In this paper,we propose,analyze and numerically validate a conservative finite element method for the nonlinear Schrodinger equation.A scalar auxiliary variable(SAV)is introduced to reformulate the nonlinear Schrodinger equation into an equivalent system and to transform the energy into a quadratic form.We use the standard continuous finite element method for the spatial discretization,and the relaxation Runge-Kutta method for the time discretization.Both mass and energy conservation laws are shown for the semi-discrete finite element scheme,and also preserved for the full-discrete scheme with suitable relaxation coefficient in the relaxation Runge-Kutta method.Numerical examples are presented to demonstrate the accuracy of the proposed method,and the conservation of mass and energy in long time simulations.
基金
Yi’s research was partially supported by NSFC Project(No.12071400)
China’s National Key R&D Programs(No.2020YFA0713500)
Hunan Provincial NSF Project Yi’s research was partially supported by NSFC Project(No.12071400)
China’s National Key R&D Programs(No.2020YFA0713500)
Hunan Provincial NSF Project。
