A Priori error estimates of Runge-Kutta discontinuous Galerkin schemes to smooth solutions of fractional

We give a priori error estimates of second order in time fully explicit Runge-Kutta discontinuous Galerkin schemes using upwind fluxes to smooth solutions of scalar fractional conservation laws in one space dimension. Under the time step restrictions tau <= ch for piecewise linear and tau less than or similar to h(4/3) for higher order finite elements, we prove a convergence rate for the energy norm & Vert;& sdot;& Vert;L-t infinity L(x)2+|& sdot;|L(x)2H(x)lambda/2 that is optimal for solutions and flux functions that are smooth enough. Our proof relies on a novel upwind projection of the exact solution.