Error analysis of the cubic front tracking and RKDG method for one dimensional conservation laws

The error analysis for the Runge-Kutta discontinuous Galerkin (RKDG) method for solving the scalar nonlinear conservation laws for the case of a smooth solution has been given in [23] and for the case of having a fully developed shock has given in [22]. We use the Cubic Front Tracking and RKDG method to obtain the solution for the case between [23] and [22] where a shock is forming but not fully developed yet. The numerical smoothness approach used in [23] is generalized for the case between [23] and [22]