@Article{AAMM-12-1,
author = {Yao, Changhui and Shi, Dongyang and Mengmeng, Hou},
title = {Superconvergence Analysis for the Maxwell's Equations in Debye Medium with a Thermal Effect},
journal = {Advances in Applied Mathematics and Mechanics},
year = {2020},
volume = {12},
number = {1},
pages = {141--163},
abstract = {<p style="text-align: justify;">In this paper, a mixed finite element method is investigated for the Maxwell&#39;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&gt;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.</p>},
issn = {2075-1354},
doi = {https://doi.org/10.4208/aamm.OA-2019-0126},
url = {https://global-sci.com/article/73029/superconvergence-analysis-for-the-maxwells-equations-in-debye-medium-with-a-thermal-effect}
}