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We study convergence of a mixed finite element-finite volume scheme for thecompressible Navier Stokes equations in the isentropic regime under the fullrange of the adiabatic coefficient gamma for the problem with general non zeroinflow/outflow boundary conditions. We propose a modification of Karper scheme[Numer. Math. 125:441-510, 2013] in order to accommodate the non zero boundarydata, prove existence of its solutions, establish the stability and uniformestimates, derive a convenient consistency formulation of the balance laws anduse it to show the weak convergence of the numerical solutions to a dissipativesolution with the Reynold defect introduced in Abbatiello et al. [PreprintArxiv 1912.12896]. If the target system admits a strong solution then theconvergence is strong towards the strong solution. Moreover, we establish theconvergence rate of the strong convergence in terms of the size of the spacediscretization h (which is supposed to be comparable with the time step). Inthe case of non zero inflow/outflow boundary data, all results are new. Thelatter result is new also for the no-slip boundary conditions.

Consistency, convergence and error estimates for a mixed finite element  / finite volume scheme to compressible Navier-Stokes equations with general  inflow/outflow boundary data