350 research outputs found
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 [Albrecht, Haasdonk, Kaulmann, Ohlberger
(2012): The localized reduced basis multiscale 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
and the online parameter simultaneously. We formulate the LRBMS based on
a generalization of the SWIPDG discretization presented in [Ern, Stephansen,
Vohralik (2010): Guaranteed and robust discontinuous Galerkin a posteriori
error estimates for convection-diffusion-reaction problems] 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, 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
Robust Numerical Methods for Singularly Perturbed Differential Equations--Supplements
The second edition of the book "Roos, Stynes, Tobiska -- Robust Numerical
Methods for Singularly Perturbed Differential Equations" appeared many years
ago and was for many years a reliable guide into the world of numerical methods
for singularly perturbed problems. Since then many new results came into the
game, we present some selected ones and the related sources.Comment: arXiv admin note: text overlap with arXiv:1909.0827
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