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An application of global approximations in the finite element method
Author(s) -
Allen E. J.
Publication year - 1985
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.1620211002
Subject(s) - finite element method , mixed finite element method , extended finite element method , function (biology) , mathematics , smoothed finite element method , finite element limit analysis , product (mathematics) , mathematical analysis , boundary knot method , geometry , physics , evolutionary biology , boundary element method , biology , thermodynamics
A technique is described in which global approximations are used to improve the accuracy of the finite element method. The technique is theoretically based on two corollaries to the Lax–Milgram lemma which are presented in this paper. Basically, the technique consists of factoring the unknown function for which an approximation is desired into the product of a global approximation and a second unknown function. Finite element methods are appropriately applied to obtain an approximation to the second unknown function. The approximation to the original function then consists of the product of the specified global approximation and the approximation to the second unknown function. The advantage that finite element methods possess with respect to obtaining banded matrices is preserved in this technique. In addition, numerical examples indicate that the technique's accuracy is as much as a factor of fifty better than the accuracy obtained by directly applying a finite element method to approximate the original function.