TY - JOUR
T1 - Gradient Recovery-Type a Posteriori Error Estimates for Steady-State Poisson-Nernst-Planck Equations
AU - Shen , Ruigang
AU - Shu , Shi
AU - Yang , Ying
AU - Fang , Mingjuan
JO - Advances in Applied Mathematics and Mechanics
VL - 6
SP - 1353
EP - 1383
PY - 2020
DA - 2020/09
SN - 12
DO - http://doi.org/10.4208/aamm.OA-2019-0046
UR - https://global-sci.org/intro/article_detail/aamm/18292.html
KW - Poisson-Nernst-Planck equations, gradient recovery, a posteriori error estimate.
AB - <p style="text-align: justify;">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.</p>