A monotone $Q^1$ finite element method for anisotropic elliptic equations
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2023
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| _version_ | 1866909270048505856 |
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| author | Li, Hao Zhang, Xiangxiong |
| author_facet | Li, Hao Zhang, Xiangxiong |
| contents | We construct a monotone continuous $Q^1$ finite element method on the uniform mesh for the anisotropic diffusion problem with a diagonally dominant diffusion coefficient matrix. The monotonicity implies the discrete maximum principle. Convergence of the new scheme is rigorously proven. On quadrilateral meshes, the matrix coefficient conditions translate into specific mesh constraints. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2310_16274 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | A monotone $Q^1$ finite element method for anisotropic elliptic equations Li, Hao Zhang, Xiangxiong Numerical Analysis 65N30, 65N15, 65N12 We construct a monotone continuous $Q^1$ finite element method on the uniform mesh for the anisotropic diffusion problem with a diagonally dominant diffusion coefficient matrix. The monotonicity implies the discrete maximum principle. Convergence of the new scheme is rigorously proven. On quadrilateral meshes, the matrix coefficient conditions translate into specific mesh constraints. |
| title | A monotone $Q^1$ finite element method for anisotropic elliptic equations |
| topic | Numerical Analysis 65N30, 65N15, 65N12 |
| url | https://arxiv.org/abs/2310.16274 |