A Conservative SAV-RRK Finite Element Method for the Nonlinear Schrodinger Equation

作     者：Jun Yang Nianyu Yi 

作者机构：School of Mathematics and Computational ScienceXiangtan UniversityXiangtanHunan 411105China Hunan Key Laboratory for Computation and Simulation in Science and EngineeringXiangtan UniversityXiangtanHunan 411105China 

出 版 物：《Advances in Applied Mathematics and Mechanics》 (应用数学与力学进展（英文）)

年 卷 期：2023年第15卷第3期

页      面：583-601页

核心收录：

学科分类：07[理学] 070102[理学-计算数学] 0701[理学-数学] 

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 

主　　题：Schrodinger equation mass conservation energy conservation finite element method relaxation Runge-Kutta scalar auxiliary variable 

摘      要：*** 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 *** use the standard continuous finite element method for the spatial discretization,and the relaxation Runge-Kutta method for the time *** 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 *** examples are presented to demonstrate the accuracy of the proposed method,and the conservation of mass and energy in long time simulations.