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一类线性Poisson-Boltzmann方程的虚单元法

陈键铧, 阳莺   

  1. 桂林电子科技大学数学与计算科学学院, 桂林 541004
  • 收稿日期:2020-01-09 出版日期:2021-09-15 发布日期:2021-09-17
  • 通讯作者: 阳莺,E-mail:angying@lsec.cc.ac.cn
  • 基金资助:
    国家自然科学基金(11561016,11661027,11701119);广西自然科学基金(2020GXNSFAA159098,2017GXNSFBA198056,2017GXNSFFA198012);广西高校数据分析与计算重点实验室开放基金;湘潭大学科学工程计算与数值仿真湖南省重点实验室开放课题基金;广西研究生教育创新计划项目(YCSW2019145);桂林电子科技大学研究生培优项目(2020YJSPYA02)资助.

陈键铧, 阳莺. 一类线性Poisson-Boltzmann方程的虚单元法[J]. 数值计算与计算机应用, 2021, 42(3): 237-246.

Chen Jianhua, Yang Ying. VIRTUAL ELEMENT METHOD FOR A CLASS OF LINEAR POISSON-BOLTZMANN EQUATION[J]. Journal on Numerica Methods and Computer Applications, 2021, 42(3): 237-246.

VIRTUAL ELEMENT METHOD FOR A CLASS OF LINEAR POISSON-BOLTZMANN EQUATION

Chen Jianhua, Yang Ying   

  1. School of Mathematics and Computing Science, Guilin University of Electronic Technology, Guilin 541004, China
  • Received:2020-01-09 Online:2021-09-15 Published:2021-09-17
Poisson-Boltzmann方程是一类带有Dirac分布源和间断系数的偏微分方程,本文主要研究一类线性的Poisson-Boltzmann方程的虚单元法.首先对Poisson-Boltzmann方程进行分解,将原方程转化为一类非奇性正则化Poisson-Boltzmann方程来求解,接着设计了相应的虚单元法.理论上给出最低阶虚单元法在H1范数下的最优误差估计.数值算例验证了理论分析的收敛阶,同时也说明了利用虚单元法可以实现线性Poisson-Boltzmann方程在多边形网格上的求解.
Poisson-Boltzmann equation is a kind of partial differential equation with Dirac distributed source and discontinuous coefficient, this paper mainly studies the virtual element method of a linear Poisson-Boltzmann equation. First, the Poisson-Boltzmann equation is decomposed, and the original equation is transformed into a class of non-singular regularized Poisson-Boltzmann equations, then, the corresponding virtual element method is designed. Theoretically, the optimal error estimation of the lowest order virtual element method under H1 norm is given. Numerical examples verify the convergence order of the theoretical analysis, it also shows that the virtual element method can be used to solve the linear Poisson-Boltzmann equation on a polygon mesh.

MR(2010)主题分类: 

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