- Journal Article
Rights / licenseIn Copyright - Non-Commercial Use Permitted
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. Show more
Journal / seriesBIT Numerical Mathematics
Pages / Article No.
SubjectShape gradients; Shape calculus; Finite element approximations; Duality techniques; 65D15; 65N30; 49Q12
Organisational unit03632 - Hiptmair, Ralf / Hiptmair, Ralf
NotesIt was possible to publish this article open access thanks to a Swiss National Licence with the publisher.
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