The Applications of Gradient Recovery to Steady-state Poisson-Nernst-Planck Equations
报告题目(Title)：The Applications of Gradient Recovery to Steady-state Poisson-Nernst-Planck Equations
报告人(Speaker)：阳莺（桂林电子科技大学）
地点(Place)：后主楼1129
时间(Time)：2021年7月9日10:00-11:00
邀请人(Inviter)：纪光华，陈华杰
报告摘要
Poisson-Nernst-Planck (PNP) equations are a coupled system of nonlinear partial differential equations which describe the electrodiffusion of ions, and are applied in many systems such as the solvated biomolecular system, the semiconductors devices, electrochemical systems and biological membrane channel. In this talk, two applications of gradient recovery are introduced for the steady-state PNP Equations. First, some superconvergence results by using the gradient recovery operator are presented for a class of strong nonlinear PNP model. It is numerically illustrated that the gradient recovery technique can be successfully applied to the computation of the practical ion channel problem to improve the efficiency of the external iteration and save CPU time. Second, the a posteriori error estimators are introduced for a class of steady-state PNP equations. Using the gradient recovery operator, the upper and lower bounds of the a posteriori error estimators are established both for the electrostatic potential and concentrations. Numerical experiments including the application to the biological ion channel problem show that the error estimators are reliable and the associated adaptive computation is efficient for the steady-state PNP systems.
