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Mathematical Problems in EngineeringVolume 2014 2014, Article ID 560492, 12 pages

Research ArticleBasic and Environmental Sciences Department, Engineering School of Lorena, University of São Paulo, 12602-810 Lorena, SP, Brazil

Received 16 April 2014; Revised 2 July 2014; Accepted 11 July 2014; Published 13 August 2014

Academic Editor: Weizhong Dai

Copyright © 2014 Estaner Claro Romão. 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 Galerkin Finite Element Method GFEM with 8- and 27-node hexahedrons elements is used for solving diffusion and transient three-dimensional reaction-diffusion with singularities. Besides analyzing the results from the primary variable temperature, the finite element approximations were used to find the derivative of the temperature in all three directions. This technique does not provide an order of accuracy compatible with the one found in the temperature solution; thereto, a calculation from the third order finite differences is proposed here, which provide the best results, as demonstrated by the first two applications proposed in this paper. Lastly, the presentation and the discussion of a real application with two cases of boundary conditions with singularities are proposed.

Autor: Estaner Claro Romão

Fuente: https://www.hindawi.com/


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