High order central discontinuous Galerkin-finite element methods for the Camassa-Holm equation

In this paper, we consider the numerical approximation of the Camassa-Holm equation which supports peakon solutions. We develop and test a high order central discontinuous Galerkin-finite element methods for solving this equation. In our numerical approach, we first reformulate the Camassa-Holm equation into a conservation law coupled with an elliptic equation. Then we propose a family of high order numerical methods which discretize the conservation law with central discontinuous Galerkin methods and the elliptic equation with continuous finite element methods. Numerical tests are presented to illustrate the accuracy and robustness of the proposed schemes.