A Superconvergent Temperature Patch Procedure for Nodal Flux Recovery in Finite Element Computations

Abstract

This article shows a new procedure for the evaluation of nodal flux fields in heat transfer analyses. Although, in principle, the idea can be easily adapted to discretization procedures other than the Finite Element Method (FEM), the numerical properties observed herein cannot be taken as universal. In the FEM framework, the proposed method shows a behavior similar to the SPR method introduced by Zhu and Zienkiewicz, especially with respect to low mesh distortion sensitivity and high convergence rate. As an advantage, the present method is computationally more efficient. The method can also be applied to elasticity or thermoelasticity problems in order to recover stresses, in which case the enhanced efficiency is even more significant. The qualitative behavior of the proposed technique is discussed using 2D conduction problems with prescribed temperature and flux boundary conditions.