A PHYSICAL INTERPRETATION OF CONVENTIONAL FINITE-ELEMENT FORMULATIONS OF CONDUCTION-TYPE PROBLEMS

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 errors. 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.