AbstractFornberg and Meyer-Spasche proposed some time ago a simple strategy to correct finite difference schemes in the presence of a free boundary that cuts across a Cartesian grid. We show here how this procedure can be combined with a minimax-based optimization procedure to rapidly solve a wide range of elliptic-type free boundary value problems. © 2009 Elsevier B.V. All rights reserved.
CitationFornberg B (2010) A finite difference method for free boundary problems. Journal of Computational and Applied Mathematics 233: 2831–2840. Available: http://dx.doi.org/10.1016/j.cam.2009.11.028.
SponsorsThe present work was supported by the NSF Grants DMS-0611681, DMS-0914647 and ATM-0620068. A significant part of the present work was carried out while the author was a Vising Fellow at OCCAM (Oxford Centre for Collaborative Applied Mathematics) under support provided by Award No. KUK-C1-013-04 to the University of Oxford, UK, by King Abdullah University of Science and Technology (KAUST).