Equal-order finite element method for the Stokes equations with variable viscosity

In this brief note, we extend the initial investigation proposed in John et al. (2016) to study the Stokes equations with variable viscosity considering a stabilized finite element scheme based on equal order polynomials for approximating the velocity and the pressure. We establish optimal a priori error estimates for this new stabilized scheme, which are further confirmed by numerical tests. Moreover, these tests show a weak viscosity dependence in the error bounds for different orders of magnitude between max and min.