一类含时Poisson-Nernst-Planck方程的虚单元计算  

A virtual element methods for a class of time-dependent Poisson-Nernst-Planck equations

作　　者：刘亚 阳莺[1,2] LIU Ya;YANG Ying(School of Mathematics and Computing Science,Guilin University of Electronic Technology,Guilin 541004,China;Center for Applied Mathematics of Guangxi,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,广西桂林541004 [2]桂林电子科技大学广西应用数学中心,广西桂林541004

出　　处：《桂林电子科技大学学报》2024年第1期1-6,共6页Journal of Guilin University of Electronic Technology

基　　金：广西自然科学基金(2020GXNSFAA159098);国家自然科学基金(12161026);广西科技项目(桂科23023002);桂林电子科技大学研究生优秀学位论文培育项目(2020YJSPYA02)。

摘　　要：针对一类含时Poisson-Nernst-Planck(PNP)方程,为避免在解决实际问题时有限元法中的网格适应性问题,构造了L^(2)投影算子与Gummel迭代相结合的虚单元算法。该算法允许以更简单的方式设计和分析新的格式,可以灵活处理各种网格,对于多边形或多面体单元甚至非凸单元组成的网格剖分都可以很好地处理,使得虚单元法可以适应于任意多边形网格,大大降低了网格的生成难度。给出了虚单元算法在三角形网格、四边形网格、非凸网格下的数值算例。数值实验结果表明,在这3种多边形网格上,L^(2)和H^(1)模的收敛阶分别为二阶和一阶,均达到了最优阶。For a class of time-dependent Poisson-Nernst-Planck(PNP)equations,in order to avoid the mesh adaptability problem in finite element method when solving practical problems,a virtual element algorithm combining L^(2) projection operator and Gummel iteration was proposed.This method allows new formats to be designed and analyzed in a simpler manner and flexible handling of various meshes.Virtual element method can handle polygon or polyhedron elements well,even the mesh division consisting of nonconvex elements,which makes virtual element method can adapt to arbitrary polygon mesh,greatly reducing the difficulty of mesh generation.Numerical examples of virtual element algorithm under triangular mesh,quadrilateral mesh,non-convex mesh are given.Numerical experiments show that on three different grids,the convergence order of the L^(2) and H^(1) norms are second order and first order respectively,and them both reach the optimal order.

关 键 词：Poisson-Nernst-Planck方程 虚单元算法 L^(2)投影 Gummel迭代 L^(2)模 H^(1)模 

分 类 号：O246.82[理学—计算数学]