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

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.