A Numerically Stable A Posteriori Error Estimator for Reduced Basis Approximations of Elliptic Equations

Buhr A, Engwer C, Ohlberger M, Rave S

Research article in edited proceedings (conference)

Abstract

The Reduced Basis (RB) method is a well established method for the model order reduction of problems formulated as parametrized partial differential equations. One crucial requirement for the application of RB schemes is the availability of an a posteriori error estimator to reliably estimate the error introduced by the reduction process. However, straightforward implementations of standard residual based estimators show poor numerical stability, rendering them unusable if high accuracy is required. In this work we propose a new algorithm based on representing the residual with respect to a dedicated orthonormal basis, which is both easy to implement and requires little additional computational overhead. A numerical example is given to demonstrate the performance of the proposed algorithm.

Details zur Publikation

Publisher: E. Onate XO, Huerta A
Book title: 11th World Congress on Computational Mechanics, WCCM 2014, 5th European Conference on Computational Mechanics, ECCM 2014 and 6th European Conference on Computational Fluid Dynamics, ECFD 2014
Release year: 2014
Publishing company: CIMNE, Barcelona
Language in which the publication is written: English
Link to the full text: https://pdfs.semanticscholar.org/c9bb/37a94131deb46736ea96d5fae80ba11697e6.pdf?_ga=2.22675131.1217033228.1531208368-865975141.1531208368