Numerical analysis of a topology optimization problem for Stokes flow

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...

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Bibliographic Details
Published inarXiv.org
Main Authors Papadopoulos, Ioannis P A, Süli, Endre
Format Paper Journal Article
LanguageEnglish
Published Ithaca Cornell University Library, arXiv.org 13.04.2022
Subjects
Computational fluid dynamics
Computer Science - Numerical Analysis
Convergence
Finite element method
Fluid flow
Mathematics - Analysis of PDEs
Mathematics - Numerical Analysis
Numerical analysis
Numerical methods
Optimization
Stokes flow
Topology optimization
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Summary: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.
ISSN:2331-8422
DOI:10.48550/arxiv.2102.10408