A micromorphic-based artificial diffusion method for stabilized finite element approximation of convection-diffusion problems
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
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2025
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| _version_ | 1866911010466562048 |
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| author | Firooz, Soheil Reddy, B. Daya Steinmann, Paul |
| author_facet | Firooz, Soheil Reddy, B. Daya Steinmann, Paul |
| contents | We present a novel artificial diffusion method to circumvent the instabilities associated with the standard finite element approximation of convection-diffusion equations. Motivated by the micromorphic approach, we introduce an auxiliary variable, which is related to the gradient of the field of interest, and which leads to a coupled problem. Conditions for well-posedness of the resulting formulation are established. We carry out a comprehensive numerical study to compare the proposed methodology against some well-established approaches in one- and two-dimensional settings. The proposed method outperforms established approaches in general in approximating accurately the solutions to pertinent and challenging problems. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2506_14800 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A micromorphic-based artificial diffusion method for stabilized finite element approximation of convection-diffusion problems Firooz, Soheil Reddy, B. Daya Steinmann, Paul Numerical Analysis Mathematical Physics We present a novel artificial diffusion method to circumvent the instabilities associated with the standard finite element approximation of convection-diffusion equations. Motivated by the micromorphic approach, we introduce an auxiliary variable, which is related to the gradient of the field of interest, and which leads to a coupled problem. Conditions for well-posedness of the resulting formulation are established. We carry out a comprehensive numerical study to compare the proposed methodology against some well-established approaches in one- and two-dimensional settings. The proposed method outperforms established approaches in general in approximating accurately the solutions to pertinent and challenging problems. |
| title | A micromorphic-based artificial diffusion method for stabilized finite element approximation of convection-diffusion problems |
| topic | Numerical Analysis Mathematical Physics |
| url | https://arxiv.org/abs/2506.14800 |