The discontinuous Galerkin method for fractal conservation laws

Abstract

We propose, analyze, 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 toward the unique entropy solution. We present numerical results for different types of solutions of linear and nonlinear fractal conservation laws.

The first version of the paper had some mathematical errors. They are corrected in this version, and the paper has appeared online in IMA J. Numer. Anal

References in corpus (1)

• Stability of Entropy Solutions for Levy Mixed Hyperbolic-Parabolic Equations

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