A-Posteriori Error Estimates for the Localized Reduced Basis Multi-Scale Method
We present a localized a-posteriori error estimate for the Localized Reduced Basis Multi-Scale (LRBMS) method . 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  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 , 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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