Abstract: 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.

Key words: Poisson-Nernst-Planck (PNP) equations, two\, grid method,  , finite element method, linearization, symmetrization