Numerical Upscaling for Wave Equations with Time-Dependent Multiscale Coefficients

In this paper, we consider the classical wave equation with time-dependent, spatially multiscale coefficients. We propose a fully discrete computational method in spirit of localized orthogonal decomposition space backward Euler scheme time. show optimal convergence rates and time beyond assumptions spatial periodicity or scale separation Further, an adaptive update strategy for time-dependent basis. Numerical experiments illustrate theoretical results showcase practicability strategy.