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

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

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 t...

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Main Authors: Sulaeman, Erwin, Hoq, S.M. Afzal, Okhunov, Abdurahim, Badran, Marwan A A
Format: Article
Language:English
Published: Science Publishing Corporation 2018
Subjects:
TJ Mechanical engineering and machinery
Online Access:http://irep.iium.edu.my/71112/
http://irep.iium.edu.my/71112/
http://irep.iium.edu.my/71112/1/71112_Trilinear%20Finite%20Element%20Solution.pdf
id iium-71112
recordtype eprints
spelling iium-711122019-07-12T07:24:51Z http://irep.iium.edu.my/71112/ Trilinear finite element solution of three dimensional heat conduction partial differential equations Sulaeman, Erwin Hoq, S.M. Afzal Okhunov, Abdurahim Badran, Marwan A A TJ Mechanical engineering and machinery 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. Science Publishing Corporation 2018 Article PeerReviewed application/pdf en http://irep.iium.edu.my/71112/1/71112_Trilinear%20Finite%20Element%20Solution.pdf 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 https://www.sciencepubco.com/index.php/ijet/article/view/28146/14785
repository_type Digital Repository
institution_category Local University
institution International Islamic University Malaysia
building IIUM Repository
collection Online Access
language English
topic TJ Mechanical engineering and machinery
spellingShingle TJ Mechanical engineering and machinery
Sulaeman, Erwin
Hoq, S.M. Afzal
Okhunov, Abdurahim
Badran, Marwan A A
Trilinear finite element solution of three dimensional heat conduction partial differential equations
description 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.
format Article
author Sulaeman, Erwin
Hoq, S.M. Afzal
Okhunov, Abdurahim
Badran, Marwan A A
author_facet Sulaeman, Erwin
Hoq, S.M. Afzal
Okhunov, Abdurahim
Badran, Marwan A A
author_sort Sulaeman, Erwin
title Trilinear finite element solution of three dimensional heat conduction partial differential equations
title_short Trilinear finite element solution of three dimensional heat conduction partial differential equations
title_full Trilinear finite element solution of three dimensional heat conduction partial differential equations
title_fullStr Trilinear finite element solution of three dimensional heat conduction partial differential equations
title_full_unstemmed Trilinear finite element solution of three dimensional heat conduction partial differential equations
title_sort trilinear finite element solution of three dimensional heat conduction partial differential equations
publisher Science Publishing Corporation
publishDate 2018
url http://irep.iium.edu.my/71112/
http://irep.iium.edu.my/71112/
http://irep.iium.edu.my/71112/1/71112_Trilinear%20Finite%20Element%20Solution.pdf
first_indexed 2023-09-18T21:40:56Z
last_indexed 2023-09-18T21:40:56Z
_version_ 1777413135062269952

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