Localized orthogonal decomposition method for the wave equation with a continuum of scales

In this paper we propose and analyze a new multiscale method for the wave equation. The proposed method does not require any assumptions on space regularity or scale-separation and it is formulated in the framework of the Localized Orthogonal Decomposition (LOD). We derive rigorous a priori error estimates for the L-approximation properties of the method, finding that convergence rates of up to third order can be achieved. The theoretical results are confirmed by various numerical experiments.