Abstract
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.
Funding source: Deutsche Forschungsgemeinschaft
Award Identifier / Grant number: 496556642
Award Identifier / Grant number: EXC-2047/1 – 390685813
Funding statement: Funded by the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) under project number 496556642. The work of BV at University Bonn is also funded by the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) under Germany’s Excellence Strategy – EXC-2047/1 – 390685813.
Acknowledgements
Major parts of this work were accomplished while BV was affiliated with Karlsruher Institut für Technologie (KIT) and EF conducted a research internship at KIT. We thank the anonymous reviewers for their valuable remarks which helped to improve the paper.
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