Error Analysis of Finite Element Method for Poisson-Nernst-Planck Equations
Document Type
Article
Publication Date
8-1-2016
Publication Title
Advances in Applied Mathematics and Mechanics
Volume
301
First page number:
28
Last page number:
43
Abstract
In this paper we study the a priori error estimates of finite element method for the system of time-dependent Poisson–Nernst–Planck equations, and for the first time, we obtain its optimal error estimates in L∞(H1) and L2(H1) norms, and suboptimal error estimates in L∞(L2) norm, with linear element, and optimal error estimates in L∞(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.
Keywords
Poisson–Nernst–Planck equations; Finite element method; A priori error estimates; Semi-discretization; Full discretization; Crank–Nicolson scheme
Disciplines
Mathematics
Repository Citation
Sun, Y.,
Sun, P.,
Zheng, B.,
Lin, G.
(2016).
Error Analysis of Finite Element Method for Poisson-Nernst-Planck Equations.
Advances in Applied Mathematics and Mechanics, 301
28-43.
http://dx.doi.org/10.1016/j.cam.2016.01.028