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

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