High-order primal mixed finite element method for boundary-value correction on curved domain
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arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866912054109011968 |
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| author | Hou, Yongli Liu, Yi Zhao, Tengjin |
| author_facet | Hou, Yongli Liu, Yi Zhao, Tengjin |
| contents | This paper addresses the non-homogeneous Neumann boundary condition on domains with curved boundaries. We consider the Raviart-Thomas element (RTk ) of degree $k \geq 1 $on triangular mesh. on a triangular mesh. A key feature of our boundary value correction method is the shift from the true boundary to a surrogate boundary. We present a high-order version of the method, achieving an $O(h^k+1/2)$ convergence in $L^2$-norm estimate for the velocity field and an $O(h^k )$ convergence in $H^1$-norm estimate for the pressure. Finally, numerical experiments validate our theoretical results. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_00687 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | High-order primal mixed finite element method for boundary-value correction on curved domain Hou, Yongli Liu, Yi Zhao, Tengjin Numerical Analysis 65N15, 65N30 G.1.8 This paper addresses the non-homogeneous Neumann boundary condition on domains with curved boundaries. We consider the Raviart-Thomas element (RTk ) of degree $k \geq 1 $on triangular mesh. on a triangular mesh. A key feature of our boundary value correction method is the shift from the true boundary to a surrogate boundary. We present a high-order version of the method, achieving an $O(h^k+1/2)$ convergence in $L^2$-norm estimate for the velocity field and an $O(h^k )$ convergence in $H^1$-norm estimate for the pressure. Finally, numerical experiments validate our theoretical results. |
| title | High-order primal mixed finite element method for boundary-value correction on curved domain |
| topic | Numerical Analysis 65N15, 65N30 G.1.8 |
| url | https://arxiv.org/abs/2410.00687 |