Volume 12, Issue 1
Superconvergence Analysis for the Maxwell's Equations in Debye Medium with a Thermal Effect
10.4208/aamm.OA-2019-0126

Adv. Appl. Math. Mech., 12 (2020), pp. 141-163.

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• 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 N\'{e}d\'{e}lec 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.

• History

Published online: 2019-12