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Solution of free-boundary problems using finite-element/Newton methods and locally refined grids - Application to analysis of solidification microstructureA new method is presented for the solution of free-boundary problems using Lagrangian finite element approximations defined on locally refined grids. The formulation allows for direct transition from coarse to fine grids without introducing non-conforming basis functions. The calculation of elemental stiffness matrices and residual vectors are unaffected by changes in the refinement level, which are accounted for in the loading of elemental data to the global stiffness matrix and residual vector. This technique for local mesh refinement is combined with recently developed mapping methods and Newton's method to form an efficient algorithm for the solution of free-boundary problems, as demonstrated here by sample calculations of cellular interfacial microstructure during directional solidification of a binary alloy.
Document ID
Document Type
Reprint (Version printed in journal)
External Source(s)
Tsiveriotis, K. (NASA Headquarters Washington, DC United States)
Brown, R. A. (MIT Cambridge, MA, United States)
Date Acquired
August 16, 2013
Publication Date
May 15, 1993
Publication Information
Publication: International Journal for Numerical Methods in Fluids
Volume: 16
Issue: 9
ISSN: 0271-2091
Subject Category
Distribution Limits