Title

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

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