Superconvergence Analysis for the Maxwell’s Equations in Debye Medium with a Thermal Effect  

作　　者：Changhui Yao Dongyang Shi Mengmeng Hou 

机构地区：[1]School of Mathematics and Statistics,Zhengzhou University,Zhengzhou,Henan 450001,China [2]State Key Laboratory of Space Weather,Chinese Academy of Sciences,Beijing 100190,China

出　　处：《Advances in Applied Mathematics and Mechanics》2020年第1期141-163,共23页应用数学与力学进展（英文）

基　　金：supported by NSFC(Nos.11871441 and 11571389)and the Specialized Research Fund for State Key Laboratory of Space Weather(No.201916);The second author is supported by NSFC(No.11671369).

摘　　要：In this paper,a mixed finite element method is investigated for the Maxwell’s equations in Debye medium with a thermal effect.In particular,in two dimensional case,the zero order N´ed´elec element(Q01Q10),the piecewise constant space Q0 element,and the bilinear element Q11 are used to approximate the electric field E and the polarization electric field P,the magnetic field H,and the temperature field u,respectively.With the help of the high accuracy results,mean-value technique and interpolation postprocessing approach,the convergent rate O(t+h^(2))for global superconvergence results are obtained under the time step constraint t=O(h^(1+g)),g>0 by using the linearized backward Euler finite element discrete scheme.At last,a numerical experiment is given to verify the theoretical analysis and the validity of our method.

关 键 词：Maxwell’s equations thermal effect error analysis SUPERCONVERGENCE 

分 类 号：O17[理学—数学]