Stabilized finite element approximations for heat conduction in a 3-D plate with dominant thermal source

Abstract

The present work studies the finite element approximation for the heat transfer process in an opaque three-dimensional plate with a temperature-dependent source dominating the conductive operator. The adopted mechanical model assumes the existence of a heat transfer from/to the plate following Newton's law of cooling. The numerical simulations performed have attested the instability of the classical Galerkin method when subjected to very high source-dominated regimen. Usual strategies in the Engineering practice of dealing with this shortcoming proved to be inefficient. A Gradient-Galerkin/Least-Squares formulation was adopted in the numerical simulations as a remedy for the Galerkin's instability when subjected to those regimen.