Comparison of Optimum Finite Element Method vs. Differential Quadrature Method in Two-dimensional Heat Transfer Problem

(*) Corresponding author

Authors' affiliations

DOI's assignment:
the author of the article can submit here a request for assignment of a DOI number to this resource!
Cost of the service: euros 10,00 (for a DOI)


Among various numerical solution techniques, finite element method (FEM) and differential quadrature method (DQM) are two important of those. Usually elements are sub-divided uniformly in FEM (conventional FEM, CFEM) to obtain temperature distribution behavior in a fin or plate. Hence, extra computational complexity is needed to obtain a fair solution with required accuracy. In this paper, non-uniform sub-elements are considered for FEM (optimum FEM, OFEM) solution to reduce the computational complexity.  Then this OFEM is applied for the solution of two-dimensional heat transfer problem in a rectangular thin fin. The obtained results are compared with CFEM and optimum DQM (ODQM, with non-uniform mesh generation). It is found that the OFEM exhibit more accurate results than CFEM and ODQM showing its potentiality
Copyright © 2014 Praise Worthy Prize - All rights reserved.


Optimum Finite Element Method; Optimum Differential Quadrature Method; Heat Transfer Problem

Full Text:



G. Strang, G.J. Fix, An Analysis of the Finite Element Method (Prentice-Hall, Inc., 1997).

R. Tirupathi, P.E. Chandrupatla, Introduction to Finite Elements in Engineering (Prentice-Hall International, 1997).

Mathematics of Finite Element Method, 2004, Available at: (Accessed on 19 October 2006).

B. Li, Numerical Method for a Parabolic Stochastic Partial Differential Equation (Chalmers Finite Element Center, 2004).

F. Fairag, Numerical Computations of Viscous, Incompressible Flow Problems Using a Two-Level Finite Element Method, arXiv: math.NA/0109109, Vol. 1, n. 17, September 2001.

S. Park, Development and Applications of Finite Elements in Time Domain, PhD Thesis, Faculty of the Virginia Polytechnic Institute and State University, Virginia, December, 1996. Available in the Library, Virginia Polytechnic Institute and State University.

R. Bellman, J. Casti, Differential quadrature and long-term integration, J Math and Appl., Vol. 34, pp. 235-238, 1971.

R. Bellman, J. Casti, Differential quadrature: A technique for the rapid solution of nonlinear partial differential equations, J Comput Phys, Vol. 10, pp. 40-52, 1972.

C.W. Bert, S.K. Jang, A.G. Striz, Nonlinear bending analysis of orthotropic rectangular plates by the method of differential quadrature, J Comput Mech, Vol. 5, pp. 217-226, 1989.

C.W. Bert, M. Malik, Fast computing technique for the transient response of gas-lubricated journal bearings, Proceedings of the U.S. National Congress of Applied Mechanics, Seattle, WA, pp. 298, June 26-July 1, 1994.

C. Shu, W. Chen, H. Xue, H. Du, Numerical analysis of grid distribution effect on the accuracy of Differential Quadrature analysis of beams and plates by error estimation of derivative approximation, Int. Journal of Numer. Methods Engineering, Vol. 51(2), pp. 159-179, 2001.

M.M. Fakir, M.K. Mawlood, W. Asrar, S. Basri, A.A. Omar, Triangular Fin Temperature Distribution by the Method of Differential Quadrature, Journal Mekanikal, Malaysia, Vo. 15, pp. 20-31, 2003.

M.M. Fakir, Application of the Differential Quadrature Method to Problems in Engineering Mechanics, MS Thesis, Faculty of Engineering, UPM, Malaysia, April 2003. Available in the library, Universiti Putra Malaysia.


  • There are currently no refbacks.

Please send any question about this web site to
Copyright © 2005-2022 Praise Worthy Prize