A Finite Element Explicit Algorithm for Solving the Temporal Temperature Fields

Practical calculations and numerical experiments in this paper have shown that in elements relating to a common node it is acceptable and reasonable for derivaties of temperature with respect to time on nodes of those elements to be presented with one on common node,if linear interpolation shape function is taken.The relation between the derivative of temperature to time on a certain node and the temperature on other nodes around that node may therefore be established after discretization of the differential equation is made in space by the finite element method.Then an explicit scheme for calculating the temperature fields may be constructed.The obtained algebraic equations,being simple and the procedure being straight will be its two tangible advantages and its calculating will,therefore,be fast.The stability analysis by the maximum principle,as in the example quoted,proves that the stability condition is similar to that in implicit algorithms.