Given a specific low-Mach model expressed in velocity, pressure and temperature variables, we
focus our attention on the convergence of a finite volume method to approximate the solution of a
convection-diffusion equation involving a Joule term. In particular:
- we establish a discrete version of a Gagliardo-Nirenberg inequality, to apply it to the analysis
of the numerical scheme,
- we consider a discretization of the Joule term consistent with the non linear diffusion one, in
order to ensure the maximum principle on the solution,
- we prove the convergence of the numerical scheme by compactness arguments.