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

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.

References in corpus (4)

• Elliptic reconstruction and a posteriori error estimates for fully discrete linear parabolic problems
• pyMOR - Generic Algorithms and Interfaces for Model Order Reduction
• Error control for the localized reduced basis multi-scale method with adaptive on-line enrichment
• Model Reduction for Multiscale Lithium-Ion Battery Simulation

Cited by in corpus (2)

• A Localized Reduced-Order Modeling Approach for PDEs with Bifurcating Solutions
• Localized Reduced Basis Approximation of a Nonlinear Finite Volume Battery Model with Resolved Electrode Geometry