In this article, mixed element algorithms with second-order time convergence results for the two-dimensional time fractional Maxwell’s equations in the Cole–Cole dispersive medium are developed. Fully discrete mixed element systems with shifted parameters θ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\theta$$\end{document} at time t=tn-θ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$t=t_{n-\theta }$$\end{document}, which are constructed by combining the generalized BDF2-θ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\theta$$\end{document} schemes in temporal direction and a mixed element method in space direction, are formulated. For the two-dimensional case of the fractional Maxwell’s system, the algorithm implementation process based on the rectangular subdivision is shown in detail. Finally, two numerical examples are provided to confirm the validity of our method and to analyze the influence of parameters α\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\alpha$$\end{document}, θ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\theta$$\end{document} for numerical solutions.

中文翻译：

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基于位移二阶差分/有限元算法的时间分数麦克斯韦系统数值模拟

在本文中，针对 Cole-Cole 色散介质中的二维时间分数 Maxwell 方程，开发了具有二阶时间收敛结果的混合元素算法。具有移位参数的完全离散混合元素系统 θ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{ upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\theta$$\end{document} 在时间 t=tn-θ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage {wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$t=t_{n -\theta }$$\end{document}, 它们是通过结合广义 BDF2-θ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage 构建的{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\theta$$\end{document} 时间方向的方案和空间方向的混合元素方法被制定。针对分数阶麦克斯韦系统的二维情况，详细展示了基于矩形细分的算法实现过程。最后，