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arXiv · 1606.09216

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

Mario Ohlberger·Stephan Rave·Felix Schindler
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Abstract

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.

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Mario Ohlberger, Stephan Rave, Felix Schindler. 2016-06-29. True Error Control for the Localized Reduced Basis Method for Parabolic Problems. https://doi.org/10.1007/978-3-319-58786-8_11

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