A TWELVE NODED FINITE ELEMENT APPROXIMATION TO 2D-POISSON EQUATIONS WITH A DIRAC LINE SOURCE
This paper presents the finite element approach to solving the Poisson equation. Using Dirichlet boundary conditions in a two-dimensional polygonal region, the polygon to be discretized is made up of twelve-noded quadrilateral structured meshes. To arrive at a numerical solution, the smaller compon...
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Institute of Mechanics of Continua and Mathematical Sciences
2025-05-01
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| Series: | Journal of Mechanics of Continua and Mathematical Sciences |
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| Online Access: | https://jmcms.s3.amazonaws.com/wp-content/uploads/2025/05/14185407/jmcms-2505015-A-TWELVE-NODED-FINITE-ELEMENT-Shivaram.pdf |
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| author | A. M. Yogitha K. T. Shivaram |
| author_facet | A. M. Yogitha K. T. Shivaram |
| author_sort | A. M. Yogitha |
| collection | DOAJ |
| description | This paper presents the finite element approach to solving the Poisson
equation. Using Dirichlet boundary conditions in a two-dimensional polygonal region, the polygon to be discretized is made up of twelve-noded quadrilateral structured meshes. To arrive at a numerical solution, the smaller components must first be solved, and the partial answers must then be combined to provide a solution for the complete mesh. The problem finds applications in various physical domains, such as fluid dynamics, heat conduction, electrostatics, and gravitational potential. However, due to the intricate nature of the domains, which include reentrant corners, fractures, and discontinuities in the solution along the borders, it can be challenging to find exact solutions to these problems. As a result, we propose using the MAPLE-18 program to provide numerical results that corroborate our theoretical conclusions and to suggest
a twelve-noded quadrilateral mesh approach that facilitates the solution of the
problem, the performance of the Galerkin weighted finite element technique on the generic polygonal domain is demonstrated numerically by use of twelve noded quadrilateral mesh. |
| format | Article |
| id | doaj-art-0ec862d609424ca9b3d3faaa2e9ea893 |
| institution | Kabale University |
| issn | 0973-8975 2454-7190 |
| language | English |
| publishDate | 2025-05-01 |
| publisher | Institute of Mechanics of Continua and Mathematical Sciences |
| record_format | Article |
| series | Journal of Mechanics of Continua and Mathematical Sciences |
| spelling | doaj-art-0ec862d609424ca9b3d3faaa2e9ea8932025-08-20T03:30:39ZengInstitute of Mechanics of Continua and Mathematical SciencesJournal of Mechanics of Continua and Mathematical Sciences0973-89752454-71902025-05-01205263710.26782/jmcms.2025.05.00003A TWELVE NODED FINITE ELEMENT APPROXIMATION TO 2D-POISSON EQUATIONS WITH A DIRAC LINE SOURCEA. M. Yogitha0K. T. Shivaram1Department of Mathematics, Dayananda Sagar College of Engineering, Visvesvaraya Technological University, Bangalore, IndiaDepartment of Mathematics, Dayananda Sagar College of Engineering, Visvesvaraya Technological University, Bangalore, IndiaThis paper presents the finite element approach to solving the Poisson equation. Using Dirichlet boundary conditions in a two-dimensional polygonal region, the polygon to be discretized is made up of twelve-noded quadrilateral structured meshes. To arrive at a numerical solution, the smaller components must first be solved, and the partial answers must then be combined to provide a solution for the complete mesh. The problem finds applications in various physical domains, such as fluid dynamics, heat conduction, electrostatics, and gravitational potential. However, due to the intricate nature of the domains, which include reentrant corners, fractures, and discontinuities in the solution along the borders, it can be challenging to find exact solutions to these problems. As a result, we propose using the MAPLE-18 program to provide numerical results that corroborate our theoretical conclusions and to suggest a twelve-noded quadrilateral mesh approach that facilitates the solution of the problem, the performance of the Galerkin weighted finite element technique on the generic polygonal domain is demonstrated numerically by use of twelve noded quadrilateral mesh.https://jmcms.s3.amazonaws.com/wp-content/uploads/2025/05/14185407/jmcms-2505015-A-TWELVE-NODED-FINITE-ELEMENT-Shivaram.pdffemshape functiontwelve noded quadrilateral meshpolygonal domainpoisson equation |
| spellingShingle | A. M. Yogitha K. T. Shivaram A TWELVE NODED FINITE ELEMENT APPROXIMATION TO 2D-POISSON EQUATIONS WITH A DIRAC LINE SOURCE Journal of Mechanics of Continua and Mathematical Sciences fem shape function twelve noded quadrilateral mesh polygonal domain poisson equation |
| title | A TWELVE NODED FINITE ELEMENT APPROXIMATION TO 2D-POISSON EQUATIONS WITH A DIRAC LINE SOURCE |
| title_full | A TWELVE NODED FINITE ELEMENT APPROXIMATION TO 2D-POISSON EQUATIONS WITH A DIRAC LINE SOURCE |
| title_fullStr | A TWELVE NODED FINITE ELEMENT APPROXIMATION TO 2D-POISSON EQUATIONS WITH A DIRAC LINE SOURCE |
| title_full_unstemmed | A TWELVE NODED FINITE ELEMENT APPROXIMATION TO 2D-POISSON EQUATIONS WITH A DIRAC LINE SOURCE |
| title_short | A TWELVE NODED FINITE ELEMENT APPROXIMATION TO 2D-POISSON EQUATIONS WITH A DIRAC LINE SOURCE |
| title_sort | twelve noded finite element approximation to 2d poisson equations with a dirac line source |
| topic | fem shape function twelve noded quadrilateral mesh polygonal domain poisson equation |
| url | https://jmcms.s3.amazonaws.com/wp-content/uploads/2025/05/14185407/jmcms-2505015-A-TWELVE-NODED-FINITE-ELEMENT-Shivaram.pdf |
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