一类线性Poisson-Boltzmann方程的虚单元法  

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

作　　者：陈键铧 阳莺[1] Chen Jianhua;Yang Ying(School of Mathematics and Computing Science,Guilin University of Electronic Technology,Guilin 541004,China)

机构地区：[1]桂林电子科技大学数学与计算科学学院,桂林541004

出　　处：《数值计算与计算机应用》2021年第3期237-246,共10页Journal on Numerical Methods and Computer Applications

基　　金：国家自然科学基金(11561016,11661027,11701119);广西自然科学基金(2020GXNSFAA 15M98,2017GXNSFBA198056,2017GXNSFFA198012);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(YC-SW2019145);桂林电子科技大学研究生培优项目(2020YJSPYA02)资助.

摘　　要：Poisson-Boltzmann方程是一类带有Dime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H^(1)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 H^(1) 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.

关 键 词：POISSON-BOLTZMANN方程 虚单元法 误差估计 多边形网格 

分 类 号：O175.2[理学—数学]