Finite element analysis of nonlinear heat conduction problems

Abstract

Nonlinear heat conduction. problem is stated and its finiteelement and time discretizations are given. Five different.numericalmethods for the solution of nonlinear heat conduction problems aresummarized. One-dimensional programs are written for the five algorithmsand preliminary runs are performed. Accuracies of all fivemethods are seen to be quite close, but their time performances differsubstantially. Based on the results of these runs and keeping thespecial defficiencies of the five different methods in mind, Bathe'ssecant incremental solution scheme is decided to be the most favorablefor the implementation of a general purpose computer code. Two dimensionalgeneral purpose program based on this algorithm is developed.Selected problems are solved with the intention of testing the program.Results are seen to be in good agreement with those'publishedin the literature.