Comparison of variational discretizations for a convection-diffusion problem
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866910333824663552 |
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| author | Bacuta, Constantin Bacuta, Cristina Hayes, Daniel |
| author_facet | Bacuta, Constantin Bacuta, Cristina Hayes, Daniel |
| contents | For a model convection-diffusion problem, we obtain new error estimates for a general upwinding finite element discretization based on bubble modification of the test space. The key analysis tool is based on finding representations of the optimal norms on the trial spaces at the continuous and discrete levels. We analyze and compare the standard linear discretization, the saddle point least square and upwinding Petrov-Galerkin methods. We conclude that the bubble upwinding Petrov-Galerkin method is the most performant discretization for the one dimensional model. Our results for the model convection-diffusion problem can be extended for creating new and efficient discretizations for the multidimensional cases. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2402_10281 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Comparison of variational discretizations for a convection-diffusion problem Bacuta, Constantin Bacuta, Cristina Hayes, Daniel Numerical Analysis For a model convection-diffusion problem, we obtain new error estimates for a general upwinding finite element discretization based on bubble modification of the test space. The key analysis tool is based on finding representations of the optimal norms on the trial spaces at the continuous and discrete levels. We analyze and compare the standard linear discretization, the saddle point least square and upwinding Petrov-Galerkin methods. We conclude that the bubble upwinding Petrov-Galerkin method is the most performant discretization for the one dimensional model. Our results for the model convection-diffusion problem can be extended for creating new and efficient discretizations for the multidimensional cases. |
| title | Comparison of variational discretizations for a convection-diffusion problem |
| topic | Numerical Analysis |
| url | https://arxiv.org/abs/2402.10281 |