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Trilinear finite element solution of three dimensional heat conduction partial differential equations

Sulaeman, Erwin and Hoq, S.M. Afzal and Okhunov, Abdurahim and Badran, Marwan A A (2018) Trilinear finite element solution of three dimensional heat conduction partial differential equations. International Journal of Engineering & Technology (UAE), 7 (4.36). pp. 379-384. ISSN 2227-524X

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Solution of partial differential equations (PDEs) of three dimensional steady state heat conduction and its error analysis are elaborated in the present paper by using a Trilinear Galerkin Finite Element method (TGFEM). An eight-node hexahedron element model is developed for the TGFEM based on a trilinear basis function where physical domain is meshed by structured grid. The stiffness matrix of the hexahedron element is formulated by using a direct integration scheme without the necessity to use the Jacobian matrix. To check the accuracy of the established scheme, comparisons of the results using error analysis between the present TGFEM and exact solution is conducted for various number of the elements. For this purpose, analytical solution is derived in detailed for a particular heat conduction problem. The comparison shows promising result where its convergence is approximately O(h²) for matrix norms L1, L2 and L.

Item Type: Article (Journal)
Additional Information: 6427/71112
Uncontrolled Keywords: Trilinear finite element method, hexahedron finite element, Galerkin method, 3D-Laplace equation, error analysis, heat conduction
Subjects: T Technology > TJ Mechanical engineering and machinery
Kulliyyahs/Centres/Divisions/Institutes (Can select more than one option. Press CONTROL button): Kulliyyah of Engineering
Kulliyyah of Engineering > Department of Mechanical Engineering
Depositing User: Dr Erwin Sulaeman
Date Deposited: 18 Mar 2019 17:34
Last Modified: 12 Jul 2019 15:24
URI: http://irep.iium.edu.my/id/eprint/71112

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