A Finite Element Method by Patch Reconstruction for the Quad-Curl Problem Using Mixed Formulations
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arXiv
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| Auteurs principaux: | , , |
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866929417453830144 |
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| author | Li, Ruo Liu, Qicheng Zhao, Shuhai |
| author_facet | Li, Ruo Liu, Qicheng Zhao, Shuhai |
| contents | We develop a high order reconstructed discontinuous approximation (RDA) method for solving a mixed formulation of the quad-curl problem in two and three dimensions. This mixed formulation is established by adding an auxiliary variable to control the divergence of the field. The approximation space for the original variables is constructed by patch reconstruction with exactly one degree of freedom per element in each dimension and the auxiliary variable is approximated by the piecewise constant space. We prove the optimal convergence rate under the energy norm and also suboptimal $L^2$ convergence using a duality approach. Numerical results are provided to verify the theoretical analysis. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_07629 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | A Finite Element Method by Patch Reconstruction for the Quad-Curl Problem Using Mixed Formulations Li, Ruo Liu, Qicheng Zhao, Shuhai Numerical Analysis We develop a high order reconstructed discontinuous approximation (RDA) method for solving a mixed formulation of the quad-curl problem in two and three dimensions. This mixed formulation is established by adding an auxiliary variable to control the divergence of the field. The approximation space for the original variables is constructed by patch reconstruction with exactly one degree of freedom per element in each dimension and the auxiliary variable is approximated by the piecewise constant space. We prove the optimal convergence rate under the energy norm and also suboptimal $L^2$ convergence using a duality approach. Numerical results are provided to verify the theoretical analysis. |
| title | A Finite Element Method by Patch Reconstruction for the Quad-Curl Problem Using Mixed Formulations |
| topic | Numerical Analysis |
| url | https://arxiv.org/abs/2407.07629 |