Convergence and error analysis of a bi-quadratic triangular galerkin finite element model for heat conduction simulation
Present paper elaborates solution of partial differential equations (PDE) of two dimensional steady state heat conduction by using a bi quadratic triangular Galerkin’s finite element method (QGFEM). The steady state heat distribution is modeled by a two-dimensional Laplace partial differential equat...
| Main Authors: | , , , , |
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| Format: | Article |
| Language: | English English |
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Penerbit Akademia Baru
2019
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| Online Access: | http://irep.iium.edu.my/67603/ http://irep.iium.edu.my/67603/9/67603%20Convergence%20and%20error%20analysis.pdf http://irep.iium.edu.my/67603/10/67603%20Convergence%20and%20error%20analysis%20SCOPUS.pdf |
| _version_ | 1848786785537097728 |
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| author | Sulaeman, Erwin Hoq, S.M. Afzal Okhunov, Abdurahim Hilmy, Irfan Badran, Marwan A A |
| author_facet | Sulaeman, Erwin Hoq, S.M. Afzal Okhunov, Abdurahim Hilmy, Irfan Badran, Marwan A A |
| author_sort | Sulaeman, Erwin |
| building | IIUM Repository |
| collection | Online Access |
| description | Present paper elaborates solution of partial differential equations (PDE) of two dimensional steady state heat conduction by using a bi quadratic triangular Galerkin’s finite element method (QGFEM). The steady state heat distribution is modeled by a two-dimensional Laplace partial differential equations. A six-node triangular element model is developed for the QGFEM based on quadratic basis functions on the Cartesian coordinate system where physical domain is meshed by structured grid. The elemental stiffness matrix is formulated by using a direct integration scheme along the triangular domain area without the necessity to use the Jacobian matrix. Validation is conducted to an analytical solution of a rectangular plate having mixed, asymmetric boundary conditions. Comparisons of the present QGFEM results and the exact solution show promising results. The convergence of the method is presented by checking the error analysis for various number of elements used for the simulation |
| first_indexed | 2025-11-14T17:14:33Z |
| format | Article |
| id | iium-67603 |
| institution | International Islamic University Malaysia |
| institution_category | Local University |
| language | English English |
| last_indexed | 2025-11-14T17:14:33Z |
| publishDate | 2019 |
| publisher | Penerbit Akademia Baru |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | iium-676032019-07-12T08:50:40Z http://irep.iium.edu.my/67603/ Convergence and error analysis of a bi-quadratic triangular galerkin finite element model for heat conduction simulation Sulaeman, Erwin Hoq, S.M. Afzal Okhunov, Abdurahim Hilmy, Irfan Badran, Marwan A A TJ255 Heat engines Present paper elaborates solution of partial differential equations (PDE) of two dimensional steady state heat conduction by using a bi quadratic triangular Galerkin’s finite element method (QGFEM). The steady state heat distribution is modeled by a two-dimensional Laplace partial differential equations. A six-node triangular element model is developed for the QGFEM based on quadratic basis functions on the Cartesian coordinate system where physical domain is meshed by structured grid. The elemental stiffness matrix is formulated by using a direct integration scheme along the triangular domain area without the necessity to use the Jacobian matrix. Validation is conducted to an analytical solution of a rectangular plate having mixed, asymmetric boundary conditions. Comparisons of the present QGFEM results and the exact solution show promising results. The convergence of the method is presented by checking the error analysis for various number of elements used for the simulation Penerbit Akademia Baru 2019-02 Article PeerReviewed application/pdf en http://irep.iium.edu.my/67603/9/67603%20Convergence%20and%20error%20analysis.pdf application/pdf en http://irep.iium.edu.my/67603/10/67603%20Convergence%20and%20error%20analysis%20SCOPUS.pdf Sulaeman, Erwin and Hoq, S.M. Afzal and Okhunov, Abdurahim and Hilmy, Irfan and Badran, Marwan A A (2019) Convergence and error analysis of a bi-quadratic triangular galerkin finite element model for heat conduction simulation. Journal of Advanced Research in Fluid Mechanics and Thermal Sciences, 54 (1). pp. 78-86. ISSN 2289-7879 http://www.akademiabaru.com/doc/ARFMTSV54_N1_P78_86.pdf |
| spellingShingle | TJ255 Heat engines Sulaeman, Erwin Hoq, S.M. Afzal Okhunov, Abdurahim Hilmy, Irfan Badran, Marwan A A Convergence and error analysis of a bi-quadratic triangular galerkin finite element model for heat conduction simulation |
| title | Convergence and error analysis of a bi-quadratic triangular galerkin finite element model for heat conduction simulation |
| title_full | Convergence and error analysis of a bi-quadratic triangular galerkin finite element model for heat conduction simulation |
| title_fullStr | Convergence and error analysis of a bi-quadratic triangular galerkin finite element model for heat conduction simulation |
| title_full_unstemmed | Convergence and error analysis of a bi-quadratic triangular galerkin finite element model for heat conduction simulation |
| title_short | Convergence and error analysis of a bi-quadratic triangular galerkin finite element model for heat conduction simulation |
| title_sort | convergence and error analysis of a bi-quadratic triangular galerkin finite element model for heat conduction simulation |
| topic | TJ255 Heat engines |
| url | http://irep.iium.edu.my/67603/ http://irep.iium.edu.my/67603/ http://irep.iium.edu.my/67603/9/67603%20Convergence%20and%20error%20analysis.pdf http://irep.iium.edu.my/67603/10/67603%20Convergence%20and%20error%20analysis%20SCOPUS.pdf |