A Novel Primal-mixed Finite Element Approach for Heat Transfer in Solids

A new reliable primal–mixed finite element approach for the heat transfer analysis in solids, is examined in detail. The essential contribution is that both variables of interest, temperature and heat flux, are calculated simultaneously from the same system of finite element equations. In addition, as a novelty, continuity of the trial and test heat flux functions is enforced, to avoid the need for some a posteriori heat flux smoothing technique. In order to minimize the accuracy error and enable introduction of the flux constraints, tensorial character of the present finite element equations is fully respected. The proposed finite element is subjected to low and high order convergence and efficiency tests in steady state and transient heat transfer analysis, which enlighten its solvability, stability, accuracy and effectiveness, i.e. its reliability.