Explicit second-order accurate taylor-galerkin based finite element formulations for heat transfer

This paper describes an explicit second-order accurate Taylor-Galerkin based finite element formulation for transient heat transfer. The fundamental concepts and characteristics of the formulations and the associated solution methodology used is described in technical detail. The approach is based on expressing the finite difference approximation of the transient time~derivative in terms of a Taylor series expansion including higher-order time derivatives, which are then evaluated from the governing partial differential equation. The stability and accuracy of the present formulations are also examined. Comparative results of several one- and two-dimensional test problems demonstrate the applicability of the proposed formulations for general transient heat transfer analysis.