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BIT Numerical Mathematics
Published in: BIT Numerical Mathematics 3/2020

16-11-2019

Convergence analysis of Galerkin finite element approximations to shape gradients in eigenvalue optimization

Authors: Shengfeng Zhu, Xianliang Hu, Qifeng Liao

Published in: BIT Numerical Mathematics | Issue 3/2020

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Abstract

This paper concerns the accuracy of Galerkin finite element approximations to two types of shape gradients for eigenvalue optimization. Under certain regularity assumptions on domains, a priori error estimates are obtained for the two approximate shape gradients. Our convergence analysis shows that the volume integral formula converges faster and offers higher accuracy than the boundary integral formula. Numerical experiments validate the theoretical results for the problem with a pure Dirichlet boundary condition. For the problem with a pure Neumann boundary condition, the boundary formulation numerically converges as fast as the distributed type.
previous article A geometric Gauss–Newton method for least squares inverse eigenvalue problems

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Metadata
Title
Convergence analysis of Galerkin finite element approximations to shape gradients in eigenvalue optimization
Authors
Shengfeng Zhu
Xianliang Hu
Qifeng Liao
Publication date
16-11-2019
Publisher
Springer Netherlands
Published in
BIT Numerical Mathematics / Issue 3/2020
Print ISSN: 0006-3835
Electronic ISSN: 1572-9125
DOI
https://doi.org/10.1007/s10543-019-00782-3

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