Fulltext

Comparison of approximate shape gradients

Hiptmair, R. ; Paganini, A. ; Sargheini, S.

In: BIT Numerical Mathematics, 2015, vol. 55, no. 2, p. 459-485

Ajouter à la liste personnelle
    Titre
    • Comparison of approximate shape gradients
    Auteur
    • Hiptmair, R.. Seminar for Applied Mathematics, ETH Zurich, Zurich, Switzerland
    • Paganini, A.. Seminar for Applied Mathematics, ETH Zurich, Zurich, Switzerland
    • Sargheini, S.. Seminar for Applied Mathematics, ETH Zurich, Zurich, Switzerland
    Type de document
    • Postprint
    Langue
    • Anglais
    Publié dans
    • BIT Numerical Mathematics, 2015, vol. 55, no. 2, p. 459-485. Springer Netherlands
    Autre version électronique
    Identifiant OAI-PMH
    • oai:doc.rero.ch:331516
    Summary
    Shape gradients of PDE constrained shape functionals can be stated in two equivalent ways. Both rely on the solutions of two boundary value problems (BVPs), but one involves integrating their traces on the boundary of the domain, while the other evaluates integrals in the volume. Usually, the two BVPs can only be solved approximately, for instance, by finite element methods. However, when used with finite element solutions, the equivalence of the two formulas breaks down. By means of a comprehensive convergence analysis, we establish that the volume based expression for the shape gradient generally offers better accuracy in a finite element setting. The results are confirmed by several numerical experiments.