Tiihonen, Timo; Järvinen, Jari On fixed point (trial) methods for free boundary problems. (English) Zbl 0817.35135 Antontsev, S. N. (ed.) et al., Free boundary problems in continuum mechanics. International conference on free boundary problems in continuum mechanics, Novosibirsk, Russia, July 15-19, 1991. Basel: Birkhäuser. ISNM, Int. Ser. Numer. Math. 106, 339-350 (1992). Summary: We consider the trial methods for solving steady state free boundary problems. For two test examples (electrochemical machining and continuous casting) we discuss the convergence of a fixed point method. Moreover, using the techniques of shape optimization we introduce a modification of the method, which gives us superlinear convergence rate. This is also confirmed numerically.For the entire collection see [Zbl 0807.00016]. Cited in 7 Documents MSC: 35R35 Free boundary problems for PDEs 49Q10 Optimization of shapes other than minimal surfaces Keywords:electrochemical machining; trial methods; continuous casting; shape optimization; superlinear convergence rate PDFBibTeX XMLCite \textit{T. Tiihonen} and \textit{J. Järvinen}, ISNM, Int. Ser. Numer. Math. 106, 339--350 (1992; Zbl 0817.35135)