A priori error estimates of finite element method for time-dependent Poisson-Nernst-Planck equations are studied in this work. We obtain the optimal error estimates in L8(H1) and L2(H1) norms, and suboptimal error estimates in L8(L2) norm, with linear element, and optimal error estimates in L8(L2) norm with quadratic or higher-order element, for both semi- and fully discrete finite element approximations. Numerical experiments are also given to validate the theoretical results.
Revised: May 12, 2016 |
Published: August 1, 2016
Citation
Sun Y., P. Sun, B. Zheng, and G. Lin. 2016.Error analysis of finite element method for Poisson-Nernst-Planck equations.Journal of Computational and Applied Mathematics 301.PNNL-SA-114192.doi:10.1016/j.cam.2016.01.028