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