On Finite Element Approximations to a Shape Gradient Flow in Shape Optimization of Elliptic Problems
Year: 2023
Author: Chunxiao Liu, Shengfeng Zhu
Journal of Computational Mathematics, Vol. 41 (2023), Iss. 5 : pp. 956–979
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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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/jcm.2208-m2020-0142
Journal of Computational Mathematics, Vol. 41 (2023), Iss. 5 : pp. 956–979
Published online: 2023-01
AMS Subject Headings:
Copyright: COPYRIGHT: © Global Science Press
Pages: 24
Keywords: Shape optimization Shape gradient Eulerian derivative Finite element Error estimate.