Accurate a posteriori error evaluation in the reduced basis method

TL;DR

This paper identifies the source of round-off error sensitivity in the a posteriori estimator within the reduced basis method and proposes a solution to improve accuracy, demonstrated through a simple example.

Contribution

It reveals the origin of accuracy loss due to round-off errors and introduces a method to mitigate this issue in the reduced basis framework.

Findings

Identified the cause of round-off sensitivity in a posteriori estimators.

Proposed a solution that enhances estimator accuracy.

Validated the approach with a simple illustrative example.

Abstract

In the reduced basis method, the evaluation of the a posteriori estimator can become very sensitive to round-off errors. In this note, the origin of the loss of accuracy is revealed, and a solution to this problem is proposed and illustrated on a simple example.