Abstract
We present a localized a-posteriori error estimate for the Localized Reduced Basis Multi-Scale (LRBMS) method [1]. The LRBMS is a combination of numerical multi-scale methods and model reduction using reduced basis methods to efficiently reduce the computational complexity of parametric multi-scale problems with respect to the multi-scale parameter \(\varepsilon \) and the online parameter \(\mu \) simultaneously. We formulate the LRBMS based on a generalization of the SWIPDG discretization presented in [2] on a coarse partition of the domain that allows for any suitable discretization on the fine triangulation inside each coarse grid element. The estimator is based on the idea of a conforming reconstruction of the discrete diffusive flux, presented in [2], that can be computed using local information only. It is offline/online decomposable and can thus be efficiently used in the context of model reduction.
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© 2014 Springer International Publishing Switzerland
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Ohlberger, M., Schindler, F. (2014). A-Posteriori Error Estimates for the Localized Reduced Basis Multi-Scale Method. In: Fuhrmann, J., Ohlberger, M., Rohde, C. (eds) Finite Volumes for Complex Applications VII-Methods and Theoretical Aspects. Springer Proceedings in Mathematics & Statistics, vol 77. Springer, Cham. https://doi.org/10.1007/978-3-319-05684-5_41
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DOI: https://doi.org/10.1007/978-3-319-05684-5_41
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