Two-grid finite element methods for space-fractional nonlinear Schrödinger equations

IF 2.1 2区 数学 Q1 MATHEMATICS, APPLIED
Yanping Chen , Hanzhang Hu
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引用次数: 0

Abstract

A two-grid finite element method is developed for solving space-fractional nonlinear Schrödinger equations. The finite element solution in L-norm is proved bounded without any time-step size conditions (dependent on spatial-step size). Then, the optimal order error estimations of the two-grid solution in the Lp-norm are proved without any time-step size conditions. Finally, the theoretical results are verified by numerical experiments.
空间分数非线性薛定谔方程的双网格有限元方法
为求解空间分数非线性薛定谔方程开发了一种双网格有限元方法。证明了 L∞ 规范下的有限元解是有界的,不需要任何时间步长条件(取决于空间步长)。然后,在不考虑任何时间步长条件的情况下,证明了 Lp 规范下双网格解的最优阶误差估计。最后,通过数值实验验证了理论结果。
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来源期刊
CiteScore
5.40
自引率
4.20%
发文量
437
审稿时长
3.0 months
期刊介绍: The Journal of Computational and Applied Mathematics publishes original papers of high scientific value in all areas of computational and applied mathematics. The main interest of the Journal is in papers that describe and analyze new computational techniques for solving scientific or engineering problems. Also the improved analysis, including the effectiveness and applicability, of existing methods and algorithms is of importance. The computational efficiency (e.g. the convergence, stability, accuracy, ...) should be proved and illustrated by nontrivial numerical examples. Papers describing only variants of existing methods, without adding significant new computational properties are not of interest. The audience consists of: applied mathematicians, numerical analysts, computational scientists and engineers.
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