Convergence of a finite volume method to weak solutions for the compressible Navier-Stokes-Fourier system
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arXiv
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| Autori principali: | , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2026
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| _version_ | 1866917356327927808 |
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| author | Feireisl, Eduard Lukacova-Medvidova, Maria She, Bangwei Yuan, Yuhuan |
| author_facet | Feireisl, Eduard Lukacova-Medvidova, Maria She, Bangwei Yuan, Yuhuan |
| contents | We prove strong convergence of an upwind-type finite volume method to a weak solution of the Navier-Stokes-Fourier system with the Dirichlet boundary conditions. The limit solution satisfies a weak form of the mass and momentum equations, together with a weak form of the entropy and ballistic energy inequalities, and complies with the weak-strong uniqueness principle. The finite volume method uses piecewise-constant spatial approximations. The convergence proof is based on a combination of delicate consistency estimates with a careful analysis of the oscillations of numerical densities via renormalisation of the continuity equation. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_20758 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Convergence of a finite volume method to weak solutions for the compressible Navier-Stokes-Fourier system Feireisl, Eduard Lukacova-Medvidova, Maria She, Bangwei Yuan, Yuhuan Numerical Analysis 35Q30, 65M08, 65M12, 35M13, 35Q35, 74S10 We prove strong convergence of an upwind-type finite volume method to a weak solution of the Navier-Stokes-Fourier system with the Dirichlet boundary conditions. The limit solution satisfies a weak form of the mass and momentum equations, together with a weak form of the entropy and ballistic energy inequalities, and complies with the weak-strong uniqueness principle. The finite volume method uses piecewise-constant spatial approximations. The convergence proof is based on a combination of delicate consistency estimates with a careful analysis of the oscillations of numerical densities via renormalisation of the continuity equation. |
| title | Convergence of a finite volume method to weak solutions for the compressible Navier-Stokes-Fourier system |
| topic | Numerical Analysis 35Q30, 65M08, 65M12, 35M13, 35Q35, 74S10 |
| url | https://arxiv.org/abs/2603.20758 |