Numerical analysis of a topology optimization problem for Stokes flow
Abstract
T. Borrvall and J. Petersson [Topology optimization of fluids in Stokes flow, International Journal for Numerical Methods in Fluids 41 (1) (2003) 77--107] developed the first model for topology optimization of fluids in Stokes flow. They proved the existence of minimizers in the infinite-dimensional setting and showed that a suitably chosen finite element method will converge in a weak(-*) sense to an unspecified solution. In this work, we prove novel regularity results and extend their numerical analysis. In particular, given an isolated local minimizer to the infinite-dimensional problem, we show that there exists a sequence of finite element solutions, satisfying necessary first-order optimality conditions, that strongly converges to it. We also provide the first numerical investigation into convergence rates.
Cite
@article{arxiv.2102.10408,
title = {Numerical analysis of a topology optimization problem for Stokes flow},
author = {Ioannis P. A. Papadopoulos and Endre Süli},
journal= {arXiv preprint arXiv:2102.10408},
year = {2022}
}