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

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