This work is devoted to numerical analysis for transient heat transfer problems by the reduced integration and Richardson extrapolation (REQ method). This computationally efficient quadrature scheme is used to generate element matrices for functionally graded quadrilateral elements to analysis of unsteady state heat transfer. In the context of solving the finite element method (FEM) discrete formulations, the central difference method is considered for better accuracy, ensuring the reliability of the numerical solutions, since the central difference method posses stability and non-oscillatory nature, which are essential for achieving precise results. To assess the performance of the new numerical technique, the research focuses on validating the computational efficiency and accuracy that involves solving the benchmark reference problems and comparing the results with the outcomes obtained through conventional Gauss quadrature and other effective numerical methods from the existing literature. The validation process aims to demonstrate the superiority of the proposed REQ method in terms of computational speed and precision of the final results.
Jeyakarthikeyan et al. (Thu,) studied this question.