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A physical interpretation of conventional finite element formulations of conduction‐type problems
Author(s) -
Comini G.,
Giudice S. Del
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.1620320307
Subject(s) - finite element method , mathematics , mixed finite element method , thermal conduction , galerkin method , type (biology) , basis (linear algebra) , interpretation (philosophy) , extended finite element method , smoothed finite element method , mathematical analysis , element (criminal law) , boundary knot method , computer science , geometry , physics , ecology , boundary element method , biology , thermodynamics , political science , law , programming language
An essentially physical approach is utilized to derive a finite element formulation of conduction‐type problems. The same systems of algebraic equations, which are usually yielded by Galerkin or variational methods, are obtained here on the basis of energy balances which lead to conservative numerical models, both at element and at node levels. As a result, it is shown that, in conventional implementations of the finite element method for conduction‐type problems, there is no artificial creation or destruction of a conserved variable. Therefore, for such formulations, inaccuracies that arise with finite sizes of elements do not depend on non‐conservation but are due solely to approximation erros. In the paper, a clear physical interpretation is also given for all the matrices and vectors which are commonly defined in most finite element formulations of conduction‐type problems.