Error analysis of heat conduction partial differential equations using Galerkin’s Finite Element method

The present work explores an error analysis of Galerkin finite element method (GFEM) for computing steady heat conduction in order to show its convergence and accuracy. The steady state heat distribution in a planar region is modeled by two-dimensional Laplace partial differential equations. A simpl...

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Main Authors:	Hoq, S.M. Afzal, Sulaeman, Erwin, Okhunov, Abdurahim
Format:	Article
Language:	English
Published:	Indian Society of Education and Environment 2016
Subjects:	QA75 Electronic computers. Computer science
Online Access:	http://irep.iium.edu.my/54413/ http://irep.iium.edu.my/54413/ http://irep.iium.edu.my/54413/ http://irep.iium.edu.my/54413/7/54413.pdf

id	iium-54413
recordtype	eprints
spelling	iium-544132017-03-17T03:40:39Z http://irep.iium.edu.my/54413/ Error analysis of heat conduction partial differential equations using Galerkin’s Finite Element method Hoq, S.M. Afzal Sulaeman, Erwin Okhunov, Abdurahim QA75 Electronic computers. Computer science The present work explores an error analysis of Galerkin finite element method (GFEM) for computing steady heat conduction in order to show its convergence and accuracy. The steady state heat distribution in a planar region is modeled by two-dimensional Laplace partial differential equations. A simple three-node triangular finite element model is used and its derivation to form elemental stiffness matrix for unstructured and structured grid meshes is presented. The error analysis is performed by comparison with analytical solution where the difference with the analytical result is represented in the form of three vector norms. The error analysis for the present GFEM for structured grid mesh is tested on heat conduction problem of a rectangular domain with asymmetric and mixed natural-essential boundary conditions. The accuracy and convergence of the numerical solution is demonstrated by increasing the number of elements or decreasing the size of each element covering the domain. It is found that the numerical result converge to the exact solution with the convergence rates of almost O(h²) in the Euclidean L2 norm, O(h²) in the discrete perpetuity L∞norm and O(h1) in the H1 norm. Indian Society of Education and Environment 2016-09 Article PeerReviewed application/pdf en http://irep.iium.edu.my/54413/7/54413.pdf Hoq, S.M. Afzal and Sulaeman, Erwin and Okhunov, Abdurahim (2016) Error analysis of heat conduction partial differential equations using Galerkin’s Finite Element method. Indian Journal of Science and Technology, 9 (36). pp. 1-6. ISSN 0974-6846 E-ISSN 0974-5645 http://www.indjst.org/index.php/indjst/article/view/102158/73758 10.17485/ijst/2016/v9i36/102158
repository_type	Digital Repository
institution_category	Local University
institution	International Islamic University Malaysia
building	IIUM Repository
collection	Online Access
language	English
topic	QA75 Electronic computers. Computer science
spellingShingle	QA75 Electronic computers. Computer science Hoq, S.M. Afzal Sulaeman, Erwin Okhunov, Abdurahim Error analysis of heat conduction partial differential equations using Galerkin’s Finite Element method
description	The present work explores an error analysis of Galerkin finite element method (GFEM) for computing steady heat conduction in order to show its convergence and accuracy. The steady state heat distribution in a planar region is modeled by two-dimensional Laplace partial differential equations. A simple three-node triangular finite element model is used and its derivation to form elemental stiffness matrix for unstructured and structured grid meshes is presented. The error analysis is performed by comparison with analytical solution where the difference with the analytical result is represented in the form of three vector norms. The error analysis for the present GFEM for structured grid mesh is tested on heat conduction problem of a rectangular domain with asymmetric and mixed natural-essential boundary conditions. The accuracy and convergence of the numerical solution is demonstrated by increasing the number of elements or decreasing the size of each element covering the domain. It is found that the numerical result converge to the exact solution with the convergence rates of almost O(h²) in the Euclidean L2 norm, O(h²) in the discrete perpetuity L∞norm and O(h1) in the H1 norm.
format	Article
author	Hoq, S.M. Afzal Sulaeman, Erwin Okhunov, Abdurahim
author_facet	Hoq, S.M. Afzal Sulaeman, Erwin Okhunov, Abdurahim
author_sort	Hoq, S.M. Afzal
title	Error analysis of heat conduction partial differential equations using Galerkin’s Finite Element method
title_short	Error analysis of heat conduction partial differential equations using Galerkin’s Finite Element method
title_full	Error analysis of heat conduction partial differential equations using Galerkin’s Finite Element method
title_fullStr	Error analysis of heat conduction partial differential equations using Galerkin’s Finite Element method
title_full_unstemmed	Error analysis of heat conduction partial differential equations using Galerkin’s Finite Element method
title_sort	error analysis of heat conduction partial differential equations using galerkin’s finite element method
publisher	Indian Society of Education and Environment
publishDate	2016
url	http://irep.iium.edu.my/54413/ http://irep.iium.edu.my/54413/ http://irep.iium.edu.my/54413/ http://irep.iium.edu.my/54413/7/54413.pdf
first_indexed	2023-09-18T21:17:00Z
last_indexed	2023-09-18T21:17:00Z
_version_	1777411629080641536

Error analysis of heat conduction partial differential equations using Galerkin’s Finite Element method

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