USE OF THE DISCRETE MAXIMUM PRINCIPLE IN FINITE-ELEMENT ANALYSIS OF COMBINED CONDUCTION AND RADIATION IN NONPARTICIPATING MEDIA

摘要

Since closed-form solutions are virtually nonexistent, the finite-element method (FEM) is frequently used to solve the combined conduction and radiation problem in nonparticipating media. In this article a Galerkin finite-element formulation is developed for the problem. However, under certain conditions, usually when the radiative component dominates the conduction component, the finite-element solutions generated by this formulation display anomalous behaviors associated with a violation of the discrete maximum principle (DMP). In this article the DMP is used as a guideline to improve the finite-element results, and the effectiveness of this approach is demonstrated through some examples. [References: 27]