Error analysis of finite element method for Poisson-Nernst-Planck equations

被引：51

作者：

Sun, Yuzhou ^{[1
]}

Sun, Pengtao ^{[1
]}

Zheng, Bin ^{[2
]}

Lin, Guang ^{[3
]}

机构：

[1] Univ Nevada, Dept Math Sci, 4505 Maryland Pkwy, Las Vegas, NV 89154 USA

[2] Pacific NW Natl Lab, Adv Comp Math & Data Div, 902 Battelle Blvd, Richland, WA 99354 USA

[3] Purdue Univ, Dept Math, 610 Purdue Mall, W Lafayette, IN 47907 USA

来源：

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS | 2016年 / 301卷

基金：

美国国家科学基金会;

关键词：

Poisson-Nernst-Planck equations; Finite element method; A priori error estimates; Semi-discretization; Full discretization; Crank-Nicolson scheme; ASYMPTOTIC ANALYSIS; ION CHANNELS; PERMEATION; GRAMICIDIN; TRANSPORT;

D O I：

10.1016/j.cam.2016.01.028

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

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-infinity (H-1) and L-2(H-1) norms, and suboptimal error estimates in L-infinity (L-2) norm, with linear element, and optimal error estimates in L-infinity (L-2) 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. (C) 2016 Elsevier B.V. All rights reserved.

引用

页码：28 / 43

页数：16

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