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An inverse finite element method for directly formulated free boundary problems
Author(s) -
Alexandrou Andreas N.
Publication year - 1989
Publication title -
international journal for numerical methods in engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.421
H-Index - 168
eISSN - 1097-0207
pISSN - 0029-5981
DOI - 10.1002/nme.1620281012
Subject(s) - finite element method , boundary (topology) , mathematics , inverse problem , inverse , line (geometry) , feature (linguistics) , boundary value problem , field (mathematics) , mathematical analysis , geometry , structural engineering , engineering , pure mathematics , linguistics , philosophy
In free boundary problems, in addition to the primary field variables, velocity, pressure and temperature, unknown geometric parameters need to be evaluated. A characteristic feature of the problems is a demarcation line which separates two domains with different material properties. The problems are highly non‐linear and difficult to handle computationally. Here an accurate and efficient method is presented which can appropriately handle the complexities associated with these problems. The method is based on a tesselation that is constructed by isolines as characteristic co‐ordinate lines. Thus opposite sides of finite elements lie on isolines. The method allows the simultaneous determination of the location of the isolines with the primary unknowns. Its accuracy and efficiency is demonstrated in a number of one and two dimensional steady and unsteady model problems.