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True Error Control for the Localized Reduced Basis Method for Parabolic Problems

arXiv e-prints, Number 1606.09216 - 2016
Télécharger la publication : 1606.09216v3.pdf [533Ko]  
We present an abstract framework for a posteriori error estimation for approximations of scalar parabolic evolution equations, based on elliptic reconstruction techniques [10, 9, 3, 5]. In addition to its original application (to derive error estimates on the discretization error), we extend the scope of this framework to derive offline/online decomposable a posteriori estimates on the model reduction error in the context of Reduced Basis (RB) methods. In addition, we present offline/online decomposable a posteriori error estimates on the full approximation error (including discretization as well as model reduction error) in the context of the localized RB method [14]. Hence, this work generalizes the localized RB method with true error certification to parabolic problems. Numerical experiments are given to demonstrate the applicability of the approach.

Références BibTex

@Article{ORS16a,
  author       = {Ohlberger, M. and Rave, S. and Schindler, F.},
  title        = {True Error Control for the Localized Reduced Basis Method for Parabolic Problems},
  journal      = {arXiv e-prints},
  number       = {1606.09216},
  year         = {2016},
  publisher    = {arXiv [math.NA]},
  note         = {https://arxiv.org/abs/1606.09216},
  url          = \{/2016/ORS16a},
}

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