@inproceedings{HarbrechtEppler, author = {Harbrecht, Helmut and Eppler, K.}, title = {SHAPE OPTIMIZATION FOR FREE BOUNDARY PROBLEMS}, editor = {G{\"u}rlebeck, Klaus and K{\"o}nke, Carsten}, organization = {Bauhaus-Universit{\"a}t Weimar}, issn = {1611-4086}, doi = {10.25643/bauhaus-universitaet.2850}, url = {http://nbn-resolving.de/urn:nbn:de:gbv:wim2-20170314-28508}, pages = {8}, abstract = {In this paper three different formulations of a Bernoulli type free boundary problem are discussed. By analyzing the shape Hessian in case of matching data it is distinguished between well-posed and ill-posed formulations. A nonlinear Ritz-Galerkin method is applied for discretizing the shape optimization problem. In case of well-posedness existence and convergence of the approximate shapes is proven. In combination with a fast boundary element method efficient first and second order shape optimization algorithms are obtained.}, subject = {Angewandte Informatik}, language = {en} }