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 ε and the online parameter μ 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.
CITATION STYLE
Ohlberger, M., & Schindler, F. (2014). A-posteriori error estimates for the localized reduced basis multi-scale method. In Springer Proceedings in Mathematics and Statistics (Vol. 77, pp. 421–429). Springer New York LLC. https://doi.org/10.1007/978-3-319-05684-5_41
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