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arXiv · 2603.20758

Convergence of a finite volume method to weak solutions for the compressible Navier-Stokes-Fourier system

Eduard Feireisl·Maria Lukacova-Medvidova·Bangwei She·Yuhuan Yuan
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Abstract

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.

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Eduard Feireisl, Maria Lukacova-Medvidova, Bangwei She, Yuhuan Yuan. 2026-03-21. Convergence of a finite volume method to weak solutions for the compressible Navier-Stokes-Fourier system. https://arxiv.org/abs/2603.20758

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