Evaluation of time integration algorithms for the semidiscretized heat conduction equation

Abstract

Finite element space discretization of heat conduction equation is briefly outlined, stability and convergence characteristics of relevant time integration methods are discussed. For the numerical integration of the semidiscretized heat conduction equation, several computer programs implementing the adopted one and two step methods are developed. A series of experiments are made and overall nine different integration algorithms are compared on the basis of accuracy and computational efficiency. Based on the results of the experiments, it has been concluded that the Crank-Nicholson method in conjuction with the smoothing process proposed by Zienkiewicz and the two-step Galerkin and Liniger methods with the starting procedure which involves starting the method with the known steady conditions prevailing for time less than zero are superior to the other methods investigated.