The discontinuous Galerkin method for fractal conservation laws

We propose, analyse and demonstrate a discontinuous Galerkin method for fractal conservation laws. Various stability estimates are established along with error estimates for regular solutions of linear equations. Moreover, in the nonlinear case and whenever piecewise constant elements are utilized, we prove a rate of convergence towards the unique entropy solution. We present numerical results for different types of solutions of linear and nonlinear fractal conservation laws.