An Evaluation of the Use of the Finite-Element Method in the Computation of Temperature

A study is made of the accuracy and efficiency of the finite-element methods in comparison to the standard finite-difference algorithms used for the computation of temperature. Numerical tests of a linear, a quadratic, and two cubic elements indicate that the quadratic method is the most accurate and desirable of these finite-element models. It is demonstrated that for steady temperature distributions, with or without sources, the finite-element models are equivalent to the finite-difference method in execution time, inferior in core storage requirements, and may be superior in accuracy. The tests also indicate that the normal finite-difference method for variable-property steady-state problems and for constant-property transient problems may be as much as an order of magnitude faster in execution and may require an order of magnitude or more less machine core storage than the finite-element methods. The study suggests that the primary advantages of the finite-element methods are associated with the ease of inputting the required data and the capability of altering the basic accuracy of the method, and its major disadvantages are large core memory requirements and lengthy execution times, particularly for variable-property problems, and some possible inaccuracies associated with the source and transient coefficients.