LOCALIZED ORTHOGONAL DECOMPOSITION METHOD FOR THE WAVE EQUATION WITH A CONTINUUM OF SCALES.

This paper is devoted to numerical approximations for the wave equation with a multiscale character. Our approach is formulated in the framework of the Localized Orthogonal Decomposition (LOD) interpreted as a numerical homogenization with an L²-projection. We derive explicit convergence rates of the method in the L∞(L²)-, W1,∞(L²)- and L∞(H¹)-norms without any assumptions on higher order space regularity or scale-separation. The order of the convergence rates depends on further graded assumptions on the initial data. We also prove the convergence of the method in the framework of G-convergence without any structural assumptions on the initial data, i.e. without assuming that it is well-prepared. This rigorously justifies the method. Finally, the performance of the method is demonstrated in numerical experiments. [ABSTRACT FROM AUTHOR]