THE DISCRETE MAXIMUM PRINCIPLE IN FINITE-ELEMENT THERMAL RADIATION ANALYSIS

Abstract

Under certain conditions, usually intense surface heat transfer associated with radiation, finite-element solutions display anomalous behaviors. These behaviors have been traced to the violation of a discrete maximum principle. Here, necessary and sufficient conditions for satisfaction of the discrete maximum principle are discussed. Special elements that satisfy a discrete maximum principle for a wider range of parameters, thereby improving the accuracy of the solution, are introduced into standard finite-element formulations for the heat conduction equation. The improved performance of these elements is then demonstrated by means of a few examples.