Nonlinear stability of entropy flux splitting schemes on bounded domains

In this paper we show how the existence of an entropy for a system of multidimensional conservation laws naturally leads to a nonlinear stability analysis of finite volume schemes. The classical implication of the Lax theorem that consistency plus stability leads to convergence can be shown in the neighbourhood of smooth solutions. As an example we consider the Lax-Friedrichs scheme applied to the Euler equations of fluid dynamics.