Year: 2020
Author: Changhui Yao, Dongyang Shi, Mengmeng Hou
Advances in Applied Mathematics and Mechanics, Vol. 12 (2020), Iss. 1 : pp. 141–163
Abstract
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 Nédélec element $(Q_{01}\times Q_{10})$, the piecewise constant space $Q_0$ element, and the bilinear element $Q_{11}$ 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 $\mathcal{O}(\tau+h^2)$ for global superconvergence results are obtained under the time step constraint $\tau=\mathcal{O}(h^{1+\gamma}),$ $ \gamma>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.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/aamm.OA-2019-0126
Advances in Applied Mathematics and Mechanics, Vol. 12 (2020), Iss. 1 : pp. 141–163
Published online: 2020-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 23
Keywords: Maxwell's equations thermal effect error analysis superconvergence.