TY - JOUR
T1 - Optimal Rate Convergence Analysis of a Second Order Numerical Scheme for the Poisson-Nernst-Planck System
AU - Jie Ding, Cheng Wang & Shenggao Zhou
JO - Numerical Mathematics: Theory, Methods and Applications
VL - 2
SP - 607
EP - 626
PY - 2018
DA - 2018/12
SN - 12
DO - http://doi.org/10.4208/nmtma.OA-2018-0058
UR - https://global-sci.org/intro/article_detail/nmtma/12911.html
KW - 
AB - <p style="text-align: justify;">In this work, we propose and analyze a second-order accurate numerical scheme, both in time and space, for the multi-dimensional Poisson-Nernst-Planck system. Linearized stability analysis is developed, so that the second order accuracy is theoretically justified for the numerical scheme, in both temporal and spatial discretization. In particularly, the discrete $W^{1,4}$ estimate for the electric potential field, which plays a crucial role in the proof, are rigorously established. In addition, various numerical tests have confirmed the anticipated numerical accuracy, and further demonstrated the effectiveness and robustness of the numerical scheme in solving problems of practical interest.</p>