Convergence of entropy stable schemes for degenerate parabolic equations with a discontinuous convection term

Abstract

Abstract. Three-point entropy stable schemes are extended  for  partial differential equations of the degenerate convection-diffusion type where a  discontinuous space-dependent function is incorporated in the convective flux. Using the compensated compactness theory, convergence of the proposed entropy stable approximations to the entropy weak solution is proved.  Assuming the so-called potential condition in the jump discontinuities, an   estimate for  entropy functions is demonstrated.Finally, using benchmark tests  a validation of the efficiency  of the entropy stable scheme  is provided by comparison with an upwind-type solution.