(untitled) (Advances in Applied Mathematics and Mechanics, 2021)
In this article, we derive the a posteriori error estimators for a class of steady-state Poisson-Nernst-Planck 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. It is shown by theory and numerical experiments that the error estimators are reliable and the associated adaptive computation is efficient for the steady-state PNP systems.