An unfitted cut finite element method with ghost penalization and cubic-spline boundary tracking solves the shape gradient flow system for PDE-constrained optimization and achieves optimal convergence rates under stated assumptions.
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An unfitted finite element method for PDE-constrained shape optimization via shape gradient flow
An unfitted cut finite element method with ghost penalization and cubic-spline boundary tracking solves the shape gradient flow system for PDE-constrained optimization and achieves optimal convergence rates under stated assumptions.