Local discontinuous Galerkin methods for the Rosenau-Burgers equation

In this paper, a local discontinuous Galerkin(LDG) method is designed for solving the Rosenau-Burgers equation with four-order spatial derivatives. Our schemes extend the previous work of Xu and Shu [8] on solving the Camassa-Holm equations on LDG method. The L 2 stability of the LDG methods is proved for general solutions. Numerical results are shown to illustrate the capability of the LDG method.