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Finite element formulations that include particular solutions of governing equations
Author(s) -
Tabarrok B.,
Xiong Y.
Publication year - 1991
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.1620310409
Subject(s) - finite element method , homogeneous , simple (philosophy) , computation , mathematics , element (criminal law) , mixed finite element method , extended finite element method , differential equation , mathematical analysis , calculus (dental) , algorithm , engineering , structural engineering , medicine , philosophy , epistemology , combinatorics , dentistry , political science , law
The correspondence between the homogeneous and particular solutions of differential equations and the related solutions of the discrete equations is brought to light in this study. Guided by this correspondence, the trial functions for finite elements are written in two parts—one the homogeneous and the other a prescribed particular solution. It is shown that this approach allows one to simplify the computations of element matrices and also yields better results, throughout the element, than those obtained by the conventional approach. Two simple examples are provided for illustration.