This paper is concerned with a family of problems of optimization of systems governed by partial differential equations (PDE). One example is considered here: the shape optimization of a shell working in linear elasticity. The displacement field is the solution of an elliptic PDE that has a design variable in its coefficients. The criterion to be minimized depends on the design variable through the solution of the PDE. It will be solved by a descent method, which requires computation of the gradient. Since such a problem must be solved numerically, it is necessary to go through discretizations. It is possible to discretize before or after differentiating. The specific subject discussed here is the comparison between two dif ferent methods:
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