This work is concerned with the classical wave equation with a high-contrast coefficient in the spatial derivative operator. We first treat the periodic case, where we derive a new limit in the one-dimensional case. The behavior is illustrated numerically and contrasted to the higher-dimensional case. For general unstructured high-contrast coefficients, we present the Localized Orthogonal Decomposition and show a priori error estimates in suitably weighted norms. Numerical experiments illustrate the convergence rates in various settings.

翻译：本文研究空间导数算子中含高反差系数的经典波动方程。我们首先处理周期情形，在一维情形下推导出新的极限。通过数值实验展示该极限行为，并与高维情形进行对比。针对一般非结构化高反差系数，我们提出局部正交分解方法，并在适当加权的范数下给出先验误差估计。数值实验展示了不同设定下的收敛速度。