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On Distributed $H^1$ Shape Gradient Flows in Optimal Shape Design of Stokes Flows: Convergence Analysis and Numerical Applications

On Distributed $H^1$ Shape Gradient Flows in Optimal Shape Design of Stokes Flows: Convergence Analysis and Numerical Applications
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Year:    2022

Author:    Jiajie Li, Shengfeng Zhu

Journal of Computational Mathematics, Vol. 40 (2022), Iss. 2 : pp. 231–257

Abstract

We consider optimal shape design in Stokes flow using $H^1$ shape gradient flows based on the distributed Eulerian derivatives. MINI element is used for discretizations of Stokes equation and Galerkin finite element is used for discretizations of distributed and boundary $H^1$ shape gradient flows. Convergence analysis with a priori error estimates is provided under general and different regularity assumptions. We investigate the performances of shape gradient descent algorithms for energy dissipation minimization and obstacle flow. Numerical comparisons in 2D and 3D show that the distributed $H^1$ shape gradient flow is more accurate than the popular boundary type. The corresponding distributed shape gradient algorithm is more effective.

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Journal Article Details

Publisher Name:    Global Science Press

Language:    English

DOI:    https://doi.org/10.4208/jcm.2009-m2020-0020

Journal of Computational Mathematics, Vol. 40 (2022), Iss. 2 : pp. 231–257

Published online:    2022-01

AMS Subject Headings:   

Copyright:    COPYRIGHT: © Global Science Press

Pages:    27

Keywords:    Shape optimization Stokes equation Distributed shape gradient Finite element MINI element Eulerian derivative.

Author Details

Jiajie Li

Shengfeng Zhu

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