一类Poisson-Nernst-Planck方程的两网格有限元离散方法

Two-Grid Finite Element Discretization Methods for a Class of Poisson-Nernst-Planck Equations

应用两网格有限元方法离散求解一类Poisson-Nernst-Planck(PNP)方程.通过两网格离散,将耦合PNP系统解耦成较小规模的线性对称系统,可有效降低计算复杂度.理论结果表明,线性对称化的两网格算法具有与传统有限元方法相同的误差阶;数值结果表明,相比于传统有限元方法,该方法计算效率更高.

A two-grid finite element method was used to solve a class of Poisson-Nernst-Planck (PNP) equations discretely. By the two-grid discretization, the coupled PNP system was decoupled into a small scale linear symmetric system, which could effectively reduce the computational complexity. The theoretical results show that the linear symmetry two-grid algorithm has the same error order as the traditional finite element method. The numerical results show that the method has higher computational efficiency than the traditional finite element method.