Gradient Recovery Type A Posteriori Error Estimates For The Time-dependent PNP Equations And Its Application

In this paper,the gradient recovery type a posteriori error estimation for time-dependent Poisson Nernst Planck(PNP)equation is studied.Based on this estimation,an adaptive finite element algorithm is designed and applied to practical ion channel problems.It is mainly divided into the following parts:Firstly,for the time-dependent PNP equation,the gradient recovery type posterior error estimator is constructed by using the gradient recovery technique,and the upper and lower bounds of the posterior error are given.Then,based on the gradient recovery type posterior error estimator,a self-adaptive finite element algorithm is designed for the time-dependent PNP equation,and a numerical example is solved in FORTRAN environment.The results show the effectiveness and reliability of the algorithm,and verify the superconvergence of the gradient recovery type posterior error estimator.Finally,the gradient recovery posteriori error estimator and adaptive finite element algorithm are successfully applied to the numerical solution of gramicidin A ion channel.Through the numerical experiments,it is found that the effect of different posteriori error estimators guiding the adaptive encryption is similar,so we can choose the simpler estimators to guide the encryption.