Shape Optimization of the Stokes Eigenvalue Problem

Abstract

.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.Keywordsshape optimizationStokes eigenvaluedistributed shape gradientmixed finite elementerror estimateMSC codes49Q1265K1065N3065N25