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arXiv · 2210.15561

Error estimates of a finite volume method for the compressible Navier--Stokes--Fourier system

Danica Basaric·Maria Lukacova-Medvidova·Hana Mizerova·Bangwei She·Yuhuan Yuan
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Abstract

In this paper we study the convergence rate of a finite volume approximation of the compressible Navier--Stokes--Fourier system. To this end we first show the local existence of a highly regular unique strong solution and analyse its global extension in time as far as the density and temperature remain bounded. We make a physically reasonable assumption that the numerical density and temperature are uniformly bounded from above and below. The relative energy provides us an elegant way to derive a priori error estimates between finite volume solutions and the strong solution.

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Danica Basaric, Maria Lukacova-Medvidova, Hana Mizerova, Bangwei She, Yuhuan Yuan. 2022-10-27. Error estimates of a finite volume method for the compressible Navier--Stokes--Fourier system. https://arxiv.org/abs/2210.15561

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