Numerical Solution of the Heat Transfer Equation Coupled with the Darcy Flow Using the Finite Element Method
The finite element approach was utilized in this study to solve numerically the two-dimensional time-dependent heat transfer equation coupled with the Darcy flow. The Picard-Lindelöf Theorem was used to prove the existence and uniqueness of the solution. The prior and posterior error estimates are t...
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| Format: | Article |
| Language: | English |
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Wiley
2022-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2022/5108445 |
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| _version_ | 1832545906191237120 |
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| author | Mohammed Hirpho |
| author_facet | Mohammed Hirpho |
| author_sort | Mohammed Hirpho |
| collection | DOAJ |
| description | The finite element approach was utilized in this study to solve numerically the two-dimensional time-dependent heat transfer equation coupled with the Darcy flow. The Picard-Lindelöf Theorem was used to prove the existence and uniqueness of the solution. The prior and posterior error estimates are then derived for the numerical scheme. Numerical examples were provided to show the effectiveness of the theoretical results. The essential code development in this study was done using MATLAB computer simulation. |
| format | Article |
| id | doaj-art-243719a6bfa7474081e90d853701538f |
| institution | Kabale University |
| issn | 1687-0409 |
| language | English |
| publishDate | 2022-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Abstract and Applied Analysis |
| spelling | doaj-art-243719a6bfa7474081e90d853701538f2025-02-03T07:24:17ZengWileyAbstract and Applied Analysis1687-04092022-01-01202210.1155/2022/5108445Numerical Solution of the Heat Transfer Equation Coupled with the Darcy Flow Using the Finite Element MethodMohammed Hirpho0Department of MathematicsThe finite element approach was utilized in this study to solve numerically the two-dimensional time-dependent heat transfer equation coupled with the Darcy flow. The Picard-Lindelöf Theorem was used to prove the existence and uniqueness of the solution. The prior and posterior error estimates are then derived for the numerical scheme. Numerical examples were provided to show the effectiveness of the theoretical results. The essential code development in this study was done using MATLAB computer simulation.http://dx.doi.org/10.1155/2022/5108445 |
| spellingShingle | Mohammed Hirpho Numerical Solution of the Heat Transfer Equation Coupled with the Darcy Flow Using the Finite Element Method Abstract and Applied Analysis |
| title | Numerical Solution of the Heat Transfer Equation Coupled with the Darcy Flow Using the Finite Element Method |
| title_full | Numerical Solution of the Heat Transfer Equation Coupled with the Darcy Flow Using the Finite Element Method |
| title_fullStr | Numerical Solution of the Heat Transfer Equation Coupled with the Darcy Flow Using the Finite Element Method |
| title_full_unstemmed | Numerical Solution of the Heat Transfer Equation Coupled with the Darcy Flow Using the Finite Element Method |
| title_short | Numerical Solution of the Heat Transfer Equation Coupled with the Darcy Flow Using the Finite Element Method |
| title_sort | numerical solution of the heat transfer equation coupled with the darcy flow using the finite element method |
| url | http://dx.doi.org/10.1155/2022/5108445 |
| work_keys_str_mv | AT mohammedhirpho numericalsolutionoftheheattransferequationcoupledwiththedarcyflowusingthefiniteelementmethod |