A New Stabilized Formulation For Convective-Diffusive Heat Transfer

This article presents a new stabilized finite-element formulation for convective-diffusive heat transfer. A mixed temperature and temperature-flux form is proposed that possesses better stability properties as compared to the classical Galerkin form. The issue of arbitrary combinations of temperature and temperature-flux interpolation functions is addressed. Specifically, the combinations of C ° interpolations that are unstable according to the Babuska-Brezzi inf-sup condition are shown to be stable and convergent within the present framework. Based on the proposed formulation, a family of 2-D elements comprising 3- and 6-node triangles and 4- and 9-node quadrilaterals has been developed. Numerical results show the good performance of the method and confirm convergence at optimal rates.