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].


35R35 Free boundary problems for PDEs
49Q10 Optimization of shapes other than minimal surfaces