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