In this paper we develop a finite element method for acoustic wave propagation in Drude-type metamaterials. The governing equation is written as a symmetrizable hyperbolic system with auxiliary variables. The standard mixed finite elements and discontinuous finite elements are used for spatial discretization, and the Crank–Nicolson scheme is used for time discretization. The a priori error analysis of fully discrete scheme is carried out in details. Numerical experiments illustrating the theoretical results and metamaterial wave propagation, are included.

中文翻译：

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超材料中瞬态声波传播的混合方法

在本文中，我们开发了一种用于声波在Drude型超材料中传播的有限元方法。控制方程写为具有辅助变量的对称双曲系统。标准混合有限元和不连续有限元用于空间离散化，而Crank–Nicolson方案用于时间离散化。详细地进行了全离散方案的先验误差分析。包括说明理论结果和超材料波传播的数值实验。