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Advances in Mechanical Engineering
Volume 2011 (2011), Article ID 251546, 10 pages
Research Article

Meshless Local Petrov-Galerkin Method for 3D Steady-State Heat Conduction Problems

1Department of Mechanical Engineering, University of Guilan, P.O. Box 3756, Rasht, Iran
2Department of Mechanical Engineering, Takestan Branch, Islamic Azad University, Takestan, Iran
3Department of Mechanical Engineering, Shahid Bahonar University of Kerman, P.O. Box 76175-133, Kerman, Iran

Received 3 March 2011; Revised 21 July 2011; Accepted 31 July 2011

Academic Editor: A. Seshadri Sekhar

Copyright © 2011 M. J. Mahmoodabadi et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


The Meshless Local Petrov-Galerkin (MLPG) method is applied for solving the three-dimensional steady state heat conduction problems. This method is a truly meshless approach; also neither the nodal connectivity nor the background mesh is required for solving the initial boundary-value problems. The penalty method is adopted to enforce the essential boundary conditions. The moving least squares (MLS) approximation is used for interpolation schemes and the Heviside step function is chosen for representing the test function. The numerical results are compared with the exact solutions of the problem and Finite Difference Method (FDM). This comparison illustrates the accuracy as well as the capability of this method.