# Article

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Keywords:
shape optimization; penalty method; extrapolation; finite elements
Summary:
A model shape optimal design in \$\mathbb{R}^2\$ is solved by means of the penalty method with extrapolation, which enables to obtain high order approximations of both the state function and the boundary flux, thus offering a reliable gradient for the sensitivity analysis. Convergence of the proposed method is proved for certain subsequences of approximate solutions.
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