一类非线性Poisson-Nernst-Planck方程的边平均有限元计算  

An edge-averaged finite element calculation for a class of nonlinear Poisson-Nernst-Planck equations

作　　者：卢晓婷 阳莺[1] LU Xiaoting;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,广西桂林541004

出　　处：《桂林电子科技大学学报》2024年第1期81-86,共6页Journal of Guilin University of Electronic Technology

基　　金：国家自然科学基金(12161026);广西自然科学基金(2020GXNSFAA159098);广西科技项目(桂科23023002)。

摘　　要：针对一类非线性Poisson-Nernst-Planck数学模型,为提高数值求解效率并保证数值求解稳定性,推导了边平均有限元离散格式,并给出了数值求解的耦合迭代算法。在对网格进行一些适当假设的情况下,边平均有限元离散格式的刚度矩阵是一个M-阵,数值求解比标准有限元方法更稳定。数值结果表明,边平均有限元方法的L^(2)模误差收敛阶达到最优阶,且在自由度相同情况下,边平均有限元方法所用CPU时间大约是标准有限元方法的1/3。For a nonlinear Poisson-Nernst-Planck mathematical model,in order to improve the stability and efficiency of numerical solution process,the edge-averaged finite element discretization scheme is derived,and a coupled iterative algorithm for numerical solution is given.Under some mild assumptions,the stiffness matrix of edge-averaged finite element discrete scheme is an M-matrix,and the numerical solution is more stable than the standard finite element method.The numerical results show that the L^(2) norm error convergence order of the edge-averaged finite element method is optimal,and the CPU time of the edge-averaged finite element method is about one third of that of the standard finite element method under the same degrees of freedom.

关 键 词：非线性Poisson-Nernst-Planck方程 边平均有限元方法 标准有限元方法 

分 类 号：O241.82[理学—计算数学]