caa a22 4500 605497249 CHVBK 20210128100540.0 cr unu---uuuuu 210128e20150601xx s 000 0 eng 10.1007/s10543-014-0515-z doi (NATIONALLICENCE)springer-10.1007/s10543-014-0515-z Comparison of approximate shape gradients [Elektronische Daten] [R. Hiptmair, A. Paganini, S. Sargheini] 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. Springer Science+Business Media Dordrecht, 2014 Shape gradients nationallicence Shape calculus nationallicence Finite element approximations nationallicence Duality techniques nationallicence Hiptmair R. Seminar for Applied Mathematics, ETH Zurich, Zurich, Switzerland aut Paganini A. Seminar for Applied Mathematics, ETH Zurich, Zurich, Switzerland aut Sargheini S. Seminar for Applied Mathematics, ETH Zurich, Zurich, Switzerland aut BIT Numerical Mathematics Springer Netherlands 55/2(2015-06-01), 459-485 0006-3835 55:2<459 2015 55 10543 https://doi.org/10.1007/s10543-014-0515-z text/html Onlinezugriff via DOI BK010053 XK010053 XK010000 Metadata rights reserved Springer special CC-BY-NC licence nationallicence 1 research-article jats NATIONALLICENCE NATIONALLICENCE NL-springer NATIONALLICENCE 856 40 https://doi.org/10.1007/s10543-014-0515-z text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Hiptmair R. Seminar for Applied Mathematics, ETH Zurich, Zurich, Switzerland aut NATIONALLICENCE 700 1- Paganini A. Seminar for Applied Mathematics, ETH Zurich, Zurich, Switzerland aut NATIONALLICENCE 700 1- Sargheini S. Seminar for Applied Mathematics, ETH Zurich, Zurich, Switzerland aut NATIONALLICENCE 773 0- BIT Numerical Mathematics Springer Netherlands 55/2(2015-06-01), 459-485 0006-3835 55:2<459 2015 55 10543