一种三维Poisson-Nernst-Planck方程的虚单元计算

Virtual Element Computation for a Three-Dimensional Poisson-Nernst-Planck Equations

利用虚单元方法在多面体网格上求解一种三维稳态Poisson-Nernst-Planck(PNP)方程,并给出PNP方程的虚单元离散形式,推导电势方程及离子浓度方程的刚度矩阵与荷载向量的矩阵表达式.数值实验结果表明,在3种不同的多面体网格下实现了PNP方程的虚单元计算,数值解在L^(2)和H^(1)范数下均达到最优阶.

The virtual element method was used to solve a three-dimensional steady-state Poisson-Nernst-Planck(PNP)equations on polyhedral meshes.The virtual element discrete forms of the PNP equations were given,and the matrix expressions of the stiffness matrix and the load vector of the electric potential equation and ion concentration equation were derived.The numerical experimental results show that the virtual element computation of PNP equations is realized in three different polyhedral meshes,and the numerical solutions reach the optimal order in both L^(2)and H^(2)norms.