%0 Conference Proceedings
%T Approximate Riesz Representatives of Shape Gradients
%+ Eidgenössische Technische Hochschule - Swiss Federal Institute of Technology  [Zürich] (ETH Zürich)
%A Paganini, Alberto
%A Hiptmair, Ralf
%< avec comité de lecture
%( IFIP Advances in Information and Communication Technology
%B 27th IFIP Conference on System Modeling and Optimization (CSMO)
%C Sophia Antipolis, France
%Y Lorena Bociu
%Y Jean-Antoine Désidéri
%Y Abderrahmane Habbal
%I Springer International Publishing
%3 System Modeling and Optimization
%V AICT-494
%P 399-409
%8 2015-06-29
%D 2015
%R 10.1007/978-3-319-55795-3_38
%K Shape gradients
%K Finite element approximations
%Z Computer Science [cs]Conference papers
%X We study finite element approximations of Riesz representatives of shape gradients. First, we provide a general perspective on its error analysis. Then, we focus on shape functionals constrained by elliptic boundary value problems and $$H^1$$-representatives of shape gradients. We prove linear convergence in the energy norm for linear Lagrangian finite element approximations. This theoretical result is confirmed by several numerical experiments.
%G English
%Z TC 7
%2 https://inria.hal.science/hal-01626913/document
%2 https://inria.hal.science/hal-01626913/file/447583_1_En_38_Chapter.pdf
%L hal-01626913
%U https://inria.hal.science/hal-01626913
%~ IFIP
%~ IFIP-AICT
%~ IFIP-TC
%~ IFIP-TC7
%~ IFIP-CSMO
%~ IFIP-AICT-494