A finite element method for Maxwell polynomial chaos Debye model

被引：3
作者：
Yao, Changhui [1 ]
Zhou, Yuzhen [1 ]
Jia, Shanghui [2 ]
机构：
[1] Zhengzhou Univ, Sch Math & Stat, Zhengzhou 450001, Henan, Peoples R China
[2] Cent Univ Finance & Econ, Sch Stat & Math, Beijing 100081, Peoples R China
来源：
APPLIED MATHEMATICS AND COMPUTATION | 2018年 / 325卷
关键词：
Maxwell's equation; Relaxation time distribution; Polynomial chaos; Finite element method; EQUATIONS; SYSTEMS;
D O I：
10.1016/j.amc.2017.12.019
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
In this paper, a finite element method is presented to approximate Maxwell-Polynomial Chaos(PC) Debye model in two spatial dimensions. The existence and uniqueness of the weak solutions are presented firstly according with the differential equations by using the Laplace transform. Then the property of energy decay with respect to the time is derived. Next, the lowest Nedelec-Raviart-Thomas element is chosen in spatial discrete scheme and the Crank-Nicolson scheme is employed in time discrete scheme. The stability of full-discrete scheme is explored before an error estimate of accuracy O(Delta t(2) + h) is proved under the L-2-norm. Numerical experiment is demonstrated for showing the correctness of the results. (C) 2017 Elsevier Inc. All rights reserved.
引用
收藏
页码：59 / 68
页数：10
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