Higher-Order Moving Mesh Methods for PDE-Constrained Shape Optimization

We present a new approach to discretizing shape optimization problems that generalizes standard moving mesh methods to higher-order mesh deformations and that is naturally compatible with higher-order finite element discretizations of PDE-constraints. This shape optimization method is based on discretized deformation diffeomorphisms and allows for arbitrarily high resolution of shapes with arbitrary smoothness. Numerical experiments show that this method allows the solution of PDE-constrained shape optimization problems to high accuracy.