On Finite Element Approximations to a Shape Gradient Flow in Shape Optimization of Elliptic Problems (Journal of Computational Mathematics, 2023)
Shape gradient flows are widely used in numerical shape optimization algorithms. Weinvestigate the accuracy and effectiveness of approximate shape gradients flows for shapeoptimization of elliptic problems. We present convergence analysis with a priori errorestimates for finite element approximations of shape gradient flows associated with a distributed or boundary expression of Eulerian derivative. Numerical examples are presentedto verify theory and show that using the volume expression is effective for shape optimization with Dirichlet and Neumann boundary conditions.