Analysis of Error in the Solution of the 2-D Diffusion Equation by Finite Element Methods

I.F.M. Moura, E.C. Roumão, J.B.C. Silva

Abstract


This work presents a numerical solution of the two-dimensional diffusion equation in comparison with the analytical solution. The norms L2 and L1 of the error are evaluated for two variants of the finite element method: the Galerkin Finite Element Method (GFEM) and the Least-Squares Finite Element Method (LSFEM). Two applications are presented and discussed.

References


[1] V.S. Arpaci, “Conduction Heat Transfer”, Addison-Wesley Publishing Company, 1966.

T.J. Chung, “Finite Element Analysis in Fluid Dynamics”, McGraw-Hill, 1978.

G. Dhatt, G. Touzot, “The Finite Element Method”, JohnWiley & Sons, 1984.

J.Q. Feng, Application of Galerkin finite-element computations in studying electro hydrodynamic problems, Journal of Electrostatic, 51-52 (2001), 590-596.

L.E. Howle, A comparison of the reduced Galerkin and pseudo-spectral methods for simulation of steady Rayleigh-Benard convection, International Journal Heat Mass Transfer, 39, No. 12 (1996), 2401-2407.

B.N. Jiang, “The Least-Squares Finite Element Method: Theory and Applications in Computational Fluid Dynamics and Electromagnetic”, Springer, 1998.

J.N. Reddy, “An Introduction to the Finite Element Method”, Second Edition, McGraw-Hill, 1993.

E.C. Rom˜ao, “Variantes do M´etodo dos Elementos Finitos para Solu¸c˜ao de Fenˆomenos Convectivo-Difusivos Bidimensionais”, Disserta¸c˜ao de Mestrado, DEM/FEIS, UNESP, Ilha Solteira, SP, 2004.

C. Taylor,T.G. Hughes, “Finite Element Programming of the Navier-Stokes Equations”, Pineridge Press Limited, Swansea, 1981.

D. Winterscheidt, K.S. Surana, P-version least-squares finite element formulation for convection-diffusion problems, International Journal for Numerical Methods in Engineering, 36 (1993), 111-133.




DOI: https://doi.org/10.5540/tema.2008.09.02.0287

Article Metrics

Metrics Loading ...

Metrics powered by PLOS ALM

Refbacks

  • There are currently no refbacks.


Trends in Computational and Applied Mathematics

A publication of the Brazilian Society of Applied and Computational Mathematics (SBMAC)

 

Indexed in:

                       

         

 

Desenvolvido por:

Logomarca da Lepidus Tecnologia