Efficient treatment of stationary free boundary problems Original Research Article

Applied Numerical Mathematics Volume 56, Issues 10–11, October–November 2006, Pages 1326–1339 Selected Papers from the First Chilean Workshop on Numerical Analysis of Partial Differential Equations (WONAPDE 2004) Cover image Efficient treatment of stationary free boundary problems Karsten Epplera, E-mail the corresponding author, Helmut Harbrechtb, Corresponding author contact information, 1, E-mail the corresponding author a Weierstrass Institute for Applied Analysis and Stochastics, Mohrenstr. 39, 10117 Berlin, Germany b Institute of Computer Science and Applied Mathematics, Christian-Albrechts-University of Kiel, Christian-Albrechts-Platz 4, 24098 Kiel, Germany http://dx.doi.org/10.1016/j.apnum.2006.03.017, How to Cite or Link Using DOI Permissions & Reprints View full text Purchase $31.50 Abstract In the present paper we consider the efficient treatment of free boundary problems by shape optimization. We reformulate the free boundary problem as shape optimization problem. A second order shape calculus enables us to analyze the shape problem under consideration and to prove convergence of a Ritz–Galerkin approximation of the shape. We show that Newtonʹs method requires only access to the underlying state function on the boundary of the domain. We compute these data by boundary integral equations which are numerically solved by a fast wavelet Galerkin scheme. Numerical results prove that we succeeded in finding a fast and robust algorithm for solving the considered class of problems.