On Finite Element Approximations to a Shape Gradient Flow in Shape Optimization of Elliptic Problems

Authors

  • Chunxiao Liu School of Statistics and Mathematics, Shanghai Lixin University of Accounting and Finance, Shanghai 201209, China
  • Shengfeng Zhu School of Mathematical Sciences, East China Normal University, Shanghai 200241, China

DOI:

https://doi.org/10.4208/jcm.2208-m2020-0142

Keywords:

Shape optimization, Shape gradient, Eulerian derivative, Finite element, Error estimate.

Abstract

Shape gradient flows are widely used in numerical shape optimization algorithms. We investigate the accuracy and effectiveness of approximate shape gradients flows for shape optimization of elliptic problems. We present convergence analysis with a priori error estimates for finite element approximations of shape gradient flows associated with a distributed or boundary expression of Eulerian derivative. Numerical examples are presented to verify theory and show that using the volume expression is effective for shape optimization with Dirichlet and Neumann boundary conditions.

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Published

2023-05-08

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Issue

Vol. 41 No. 5 (2023)

Section

Articles

How to Cite

On Finite Element Approximations to a Shape Gradient Flow in Shape Optimization of Elliptic Problems. (2023). Journal of Computational Mathematics, 41(5), 956-979. https://doi.org/10.4208/jcm.2208-m2020-0142