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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2508.02677 |
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| _version_ | 1866913974949249024 |
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| author | Rao, B. Veena S. N. |
| author_facet | Rao, B. Veena S. N. |
| contents | This paper details the development and application of an $h$-adaptive finite element method for the numerical solution of the \textit{Falkner-Skan equation}. A posteriori error estimation governs the adaptivity of the mesh, specifically the well-established \textit{Kelly error estimator}, which utilizes the jump in the gradient across elements. The implementation of this method allowed for accurate and efficient resolution of the boundary layer behavior characteristic of Falkner-Skan flows. Numerical solutions were obtained across various wedge flow parameters, encompassing favorable and adverse pressure gradients. A key focus of this study was the precise computation of the skin friction coefficient, a critical parameter in boundary layer analysis, across this diverse range of flow conditions. The results are presented and discussed, demonstrating the robustness and accuracy of the adaptive finite element approach for this class of nonlinear boundary layer problems. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2508_02677 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Automated $h$-adaptivity for finite element approximations of the Falkner-Skan equation Rao, B. Veena S. N. Numerical Analysis This paper details the development and application of an $h$-adaptive finite element method for the numerical solution of the \textit{Falkner-Skan equation}. A posteriori error estimation governs the adaptivity of the mesh, specifically the well-established \textit{Kelly error estimator}, which utilizes the jump in the gradient across elements. The implementation of this method allowed for accurate and efficient resolution of the boundary layer behavior characteristic of Falkner-Skan flows. Numerical solutions were obtained across various wedge flow parameters, encompassing favorable and adverse pressure gradients. A key focus of this study was the precise computation of the skin friction coefficient, a critical parameter in boundary layer analysis, across this diverse range of flow conditions. The results are presented and discussed, demonstrating the robustness and accuracy of the adaptive finite element approach for this class of nonlinear boundary layer problems. |
| title | Automated $h$-adaptivity for finite element approximations of the Falkner-Skan equation |
| topic | Numerical Analysis |
| url | https://arxiv.org/abs/2508.02677 |