Error estimation and adaptivity in finite element analysis of convective heat transfer problems .1. Theoretical considerations

This is the first of two articles concerning error estimation and adaptive refinement techniques applied to convective heat transfer problems. This study presents the detailed development of the proposed error estimator. The error estimator takes into account the coupling effects of the dependent variables (e.g., velocity and temperature) on the discretization error and, consequently, on the adaptive meshes. An averaging procedure is also proposed as a substitute for the smoothing/recovery procedure used to evaluate the gradients The implementation of the averaging technique is simple and cost effective. Numerical experiments demonstrate that the proposed methodology results in a dramatic reduction in computational costs.