TY - JOUR
T1 - Superconvergence Analysis for the Maxwell's Equations in Debye Medium with a Thermal Effect
AU - Yao , Changhui
AU - Shi , Dongyang
AU - Hou , Mengmeng
JO - Advances in Applied Mathematics and Mechanics
VL - 1
SP - 141
EP - 163
PY - 2019
DA - 2019/12
SN - 12
DO - http://doi.org/10.4208/aamm.OA-2019-0126
UR - https://global-sci.org/intro/article_detail/aamm/13422.html
KW - Maxwell's equations, thermal effect, error analysis,   superconvergence.
AB - <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>