The discontinuous Galerkin method for fractal conservation laws
Simone Cifani, Espen R. Jakobsen and Kenneth H. Karlsen
Abstract: We propose, analyze, and demonstrate a discontinuous Galerkin method for fractional conservation laws. Various stability estimates are established along with error estimates for regular solutions of linear equations. Moreover, in the nonlinear case and when piecewise constant elements are utilized, we prove a rate of convergence toward the unique entropy solution. We present numerical results for different types of solutions of linear and nonlinear fractional conservation laws.