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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2504.04381 |
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| _version_ | 1866915292330852352 |
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| author | Hang, Li Li, Chenyang |
| author_facet | Hang, Li Li, Chenyang |
| contents | In this paper, we derive first-order Euler finite element discretization schemes for a time-dependent natural convection model with variable density (NCVD). The model is governed by the variable density Navier-Stokes equations coupled with a parabolic partial differential equation that describes the evolution of temperature. Stability and error estimate for the velocity, pressure, density and temperature in $L^2$-norm are proved by using finite element approximations in space and finite differences in time. Finally, the numerical results are showed to support the theoretical analysis. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_04381 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Error analysis of a Euler finite element scheme for Natural convection model with variable density Hang, Li Li, Chenyang Numerical Analysis In this paper, we derive first-order Euler finite element discretization schemes for a time-dependent natural convection model with variable density (NCVD). The model is governed by the variable density Navier-Stokes equations coupled with a parabolic partial differential equation that describes the evolution of temperature. Stability and error estimate for the velocity, pressure, density and temperature in $L^2$-norm are proved by using finite element approximations in space and finite differences in time. Finally, the numerical results are showed to support the theoretical analysis. |
| title | Error analysis of a Euler finite element scheme for Natural convection model with variable density |
| topic | Numerical Analysis |
| url | https://arxiv.org/abs/2504.04381 |