Shape gradients of shape differentiable shape functionals constrained to an interface problem (IP) can be formulated in two equivalent ways. Both formulations rely on the solution of two IPs, and their equivalence breaks down when these IPs are solved approximatively. We establish which expression for the shape gradient offers better accuracy for approximations by means of finite elements. Great effort is devoted to provide numerical evidence of the theoretical considerations.
CitationPaganini A. (2015) Approximate Shape Gradients for Interface Problems. In: Pratelli A., Leugering G. (eds) New Trends in Shape Optimization. International Series of Numerical Mathematics, vol 166. Birkhäuser, Cham
Author affiliation/Organisation/COLLEGE OF SCIENCE AND ENGINEERING/Department of Mathematics
VersionAM (Accepted Manuscript)
Published inNew Trends in Shape Optimization. International Series of Numerical Mathematics
EditorsPratelli A., Leugering G.
Book seriesInternational Series of Numerical Mathematics