# New bounding techniques for goal-oriented error estimation applied to linear problems

## TL;DR

This paper introduces new bounding techniques based on Saint-Venant's principle and homothetic domains to improve the accuracy of goal-oriented error estimates in linear problems, demonstrated through numerical experiments.

## Contribution

It presents a novel approach for error bounding in linear problems using properties of homothetic domains, enhancing the precision of error estimates.

## Key findings

- Improved error bounds for linear problems.
- Effective use of homothetic domains in error estimation.
- Numerical experiments validate the proposed techniques.

## Abstract

The paper deals with the accuracy of guaranteed error bounds on outputs of interest computed from approximate methods such as the finite element method. A considerable improvement is introduced for linear problems thanks to new bounding techniques based on Saint-Venant's principle. The main breakthrough of these optimized bounding techniques is the use of properties of homothetic domains which enables to cleverly derive guaranteed and accurate boundings of contributions to the global error estimate over a local region of the domain. Performances of these techniques are illustrated through several numerical experiments.