Enhanced Higher-Order Multiscale Method for Wave Propagation
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We propose a higher-order numerical homogenization strategy based on the higher-order localized orthogonal decomposition method to model wave propagation in highly oscillatory media. The method enriches coarse scale finite element basis functions by so-called corrections such that convergence can be shown in the regime where the fine-scale features of the diffusion coefficient are not resolved. Previously, was shown that the higher-order convergence from the elliptic setting cannot be easily transferred to the wave equation. This results from the general assumptions on the diffusion coefficient, where we only have boundedness. In this talk present a strategy that further enriches the coarse scale spaces such that even for the highly irregular setting higher-order convergence can be achieved. Further, we present a suitable localization strategy to allow for fast propagation in time and give numerical examples to confirm the theoretical findings.