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The w ‐plane finite element method for the solution of scalar field problems in two dimensions
Author(s) -
Nath B.,
Jamshidi J.
Publication year - 1980
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.1620150306
Subject(s) - finite element method , mathematical analysis , mathematics , plane (geometry) , scalar field , scalar (mathematics) , boundary value problem , nonlinear system , simple (philosophy) , domain (mathematical analysis) , homogeneity (statistics) , geometry , physics , engineering , structural engineering , mathematical physics , philosophy , statistics , epistemology , quantum mechanics
A simple, efficient finite element method has been presented for the solution of a variety of scalar field problems in two dimensions. It is based on the mapping of the physical problem domain into an ‘image’ domain in the w ‐plane. The governing equation(s) and the boundary conditions in the physical plane are also appropriately transformed into the w ‐plane. The processes of standard finite element analysis are then implemented to obtain a solution in the w ‐plane. The method has been explained in detail, with illustrative examples where appropriate; it has several important advantages over the standard finite element method, particularly for the solution of infinite or semi‐infinite domain problems. The method has been demonstrated to be simple, efficient, economical and potentially capable of dealing with a large repartoire of two‐dimensional problems, including non‐homogeneity, nonlinearity, etc.