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

被引：48
|
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
收藏
页码：28 / 43
页数：16
相关论文
共 50 条
12345