One-sided stability and convergence of the Nessyahu–Tadmor scheme

Non-oscillatory schemes are widely used in numerical approximations of nonlinear conservation laws. The Nessyahu–Tadmor (NT) scheme is an example of a second order scheme that is both robust and simple. In this paper, we prove a new stability property of the NT scheme based on the standard minmod reconstruction in the case of a scalar strictly convex conservation law. This property is similar to the One-sided Lipschitz condition for first order schemes. Using this new stability, we derive the convergence of the NT scheme to the exact entropy solution without imposing any nonhomogeneous limitations on the method. We also derive an error estimate for monotone initial data.