| Abstract: |
| In this talk, we investigate the numerical approximation of shape gradient flows arising from PDE-constrained shape optimization problems. The shape gradient flow system comprises the state equation, adjoint state equation, velocity equation,
and domain evolution map. For discretization, we discuss two strategies: evolving finite element method where the mesh adapts dynamically to the evolving domain using evolving finite elements, as well as unfitted finite element method by use of a fixed background mesh enhanced with cubic splines to implicitly track domain boundaries. For both approaches, we derive
rigorous a priori error estimates. Numerical experiments are provided to validate these theoretical findings. |
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