量子力学扰动波方程的结构保持有限元模型

IF 2.9 2区数学 Q1 MATHEMATICS, APPLIED

Applied Mathematics Letters Pub Date : 2024-06-06 DOI:10.1016/j.aml.2024.109189

Junjun Wang , Rui Chen , Wenjing Ma , Weijie Zhao

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引用次数: 0

摘要

本文展示了用于计算量子力学扰动波方程的保结构有限元法（FEM）的构建和分析。首先，建立了一个新的全离散系统，并证明其在能量意义上是保守的。同时，推导了数值解的有界性。其次，借助布劳威尔定点定理和一些特殊的分裂技术，得到了解的存在性和唯一性。第三，我们提供了全面的超近分析，给出了全局超收敛结果。最后，我们给出了数值结果来说明理论分析。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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Structure preserving FEM for the perturbed wave equation of quantum mechanics

The construction and analysis of structure-preserving finite element method (FEM) for computing the perturbed wave equation of quantum mechanics are demonstrated. Firstly, a new fully discrete system is built and proved conservative in the sense of the energy. Meanwhile, the boundedness of the numerical solution is derived. Secondly, the existence and uniqueness of the solution are obtained with the help of the Brouwer fixed-point theorem and some special splitting technique. Thirdly, we provide a comprehensive superclose analysis, offering the global superconvergent result. Finally, numerical results are presented to illustrate the theoretical analysis.

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来源期刊

Applied Mathematics Letters 数学-应用数学

CiteScore

7.70

自引率

5.40%

发文量

347

审稿时长

10 days

期刊介绍： The purpose of Applied Mathematics Letters is to provide a means of rapid publication for important but brief applied mathematical papers. The brief descriptions of any work involving a novel application or utilization of mathematics, or a development in the methodology of applied mathematics is a potential contribution for this journal. This journal''s focus is on applied mathematics topics based on differential equations and linear algebra. Priority will be given to submissions that are likely to appeal to a wide audience.