A recovered gradient method applied to smooth optimal shape problems
The article is devoted to sensitivity analysis in the optimal shape design. Several state problems based on elliptic boundary value problems are considered. The problems are formulated on a ``generalized rectangle'' whose upper side is formed by a design function which is a Bézier curve. The paper presents a new postprocessing technique suitable for quasiuniform triangulations which can be employed in the sensitivity analysis of optimal shape design problems. In the first part of the paper, a class of admissible domains is introduced, and the state problems and cost functionals are defined. Then, sensitivity formulae expressed by boundary integrals are derived for three standard cost functionals. There is also a section where the discretization by linear finite elements is discussed and the approximate optimization problems are defined. Finally, the authors recall the technique of recovered gradients on chevron triangulations and propose its application to the sensitivity formulae evaluation.
scientific article; zbMATH DE number 1046550