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SHAPE OPTIMIZATION OF THE STOKES EIGENVALUE PROBLEM
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DOI：10.1137/21M1451543.png)
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Abstract
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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.
Keywords:
shape optimization
Stokes eigenvalue
distributed shape gradient
mixed finite element
error estimate
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