# Certified Descent Algorithm for shape optimization driven by fully-computable a posteriori error estimators

arXiv: https://arxiv.org/abs/1604.04921 · HTML: https://mlsanity.com/paper/1604.04921/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 17 Apr 2016.

## Built on by (most cited first, 1 of 1)

- [Anisotropic mesh adaptation for region-based segmentation accounting for image spatial information](https://mlsanity.com/paper/2112.10138/) (2021)

## Abstract (arXiv)

In this paper we introduce a novel certified shape optimization strategy - named Certified Descent Algorithm (CDA) - to account for the numerical error introduced by the Finite Element approximation of the shape gradient. We present a goal-oriented procedure to derive a certified upper bound of the error in the shape gradient and we construct a fully-computable, constant-free a posteriori error estimator inspired by the complementary energy principle. The resulting CDA is able to identify a genuine descent direction at each iteration and features a reliable stopping criterion. After validating the error estimator, some numerical simulations of the resulting certified shape optimization strategy are presented for the well-known inverse identification problem of Electrical Impedance Tomography.