A priori error estimate for a well-balanced scheme designed for inhomogeneous scalar conservation laws

The aim of this Note is to derive an a-priori error estimate for the approximate solution generated by means of the numerical scheme proposed in [5] and extensively studied in [4]. This scheme belongs to the class of well-balanced schemes introduced by Greenberg and LeRoux [6]; its main features are its robustness and its ability to preserve the correct steady-states of the continuous problem. Here, we show that it is endowed with the usual O(root Delta x) error in most cases. (C) Academie des Sciences/Elsevier, Paris.