SHAPE OPTIMIZATION OF THE STOKES EIGENVALUE PROBLEM

被引：1
|
作者：
Li, Jiajie [1 ]
Zhu, Shengfeng [1 ,2 ]
机构：
[1] East China Normal Univ, Dept Math, Shanghai 200241, Peoples R China
[2] East China Normal Univ, Shanghai Key Lab Pure Math & Math Practice, Shanghai 200241, Peoples R China
来源：
SIAM JOURNAL ON SCIENTIFIC COMPUTING | 2023年 / 45卷 / 02期
基金：
中国国家自然科学基金;
关键词：
shape optimization; Stokes eigenvalue; distributed shape gradient; mixed finite element; error estimate; FINITE-ELEMENT-METHOD; APPROXIMATION; STABILITY; GRADIENTS;
D O I：
10.1137/21M1451543
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
We consider solving the Stokes eigenvalue optimization problem. Distributed and boundary types of Eulerian derivatives are derived from shape calculus. A priori error estimates for finite element discretizations of both shape gradients are shown. The approximate distributed shape gradient has better convergence and is used in numerical algorithms. We propose a single -grid algorithm and a two-grid algorithm for Stokes eigenvalue optimization. Numerical results are presented to verify theory and show effectiveness and efficiency of the algorithms proposed.
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页码：A798 / A828
页数：31
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