Galerkin finite element method for nonlinear fractional Schrodinger equations
Galerkin finite element method for nonlinear fractional Schrodinger equations
复制标题
非线性分数阶薛定谔方程的伽辽金有限元法
DOI：
10.1007/s11075-016-0160-5
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发表时间：
2017
影响因子：
2.1
通讯作者：
Wang Pengde
中科院分区：
文献类型：
--
作者：
Li Meng;Huang Chengming;Wang Pengde
本文考虑一类非线性Riesz空间分数阶Schr dinger方程。基于空间上的标准Galerkin有限元方法和时间上的Crank-Nicolson差分方法，构造了半离散和全离散系统。利用Brouwer不动点定理和分数阶Gagliardo-Nirenberg不等式，证明了完全离散系统是唯一可解的.此外，我们着重于严格的分析和考虑的半离散和全离散系统的守恒性和收敛性。最后介绍了一种线性化的有限元迭代算法，并给出了数值例子来验证理论结果。
In this paper, a class of nonlinear Riesz space-fractional Schrödinger equations are considered. Based on the standard Galerkin finite element method in space and Crank-Nicolson difference method in time, the semi-discrete and fully discrete systems are constructed. By Brouwer fixed point theorem and fractional Gagliardo-Nirenberg inequality, we prove the fully discrete system is uniquely solvable. Moreover, we focus on a rigorous analysis and consideration of the conservation and convergence properties for the semi-discrete and fully discrete systems. Finally, a linearized iterative finite element algorithm is introduced and some numerical examples are given to confirm the theoretical results.