Adaptive finite element method for shape optimization
ESAIM: Control, Optimisation and Calculus of Variations, Tome 18 (2012) no. 4, pp. 1122-1149.

We examine shape optimization problems in the context of inexact sequential quadratic programming. Inexactness is a consequence of using adaptive finite element methods (AFEM) to approximate the state and adjoint equations (via the dual weighted residual method), update the boundary, and compute the geometric functional. We present a novel algorithm that equidistributes the errors due to shape optimization and discretization, thereby leading to coarse resolution in the early stages and fine resolution upon convergence, and thus optimizing the computational effort. We discuss the ability of the algorithm to detect whether or not geometric singularities such as corners are genuine to the problem or simply due to lack of resolution - a new paradigm in adaptivity.

DOI : 10.1051/cocv/2011192
Classification : 49M25, 65M60
Mots-clés : shape optimization, adaptivity, mesh refinement/coarsening, smoothing 
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     title = {Adaptive finite element method for shape optimization},
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Morin, Pedro; Nochetto, Ricardo H.; Pauletti, Miguel S.; Verani, Marco. Adaptive finite element method for shape optimization. ESAIM: Control, Optimisation and Calculus of Variations, Tome 18 (2012) no. 4, pp. 1122-1149. doi : 10.1051/cocv/2011192. http://archive.numdam.org/articles/10.1051/cocv/2011192/

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