Local Discontinuous Galerkin Method for the Camassa-Holm Equation

摘要

In this paper, we develop, analyze and test a local discontinuous Galerkin (LDG) method for solving the Camassa-Holm equation which contains nonlinear high order derivatives. The LDG method has the flexibility for arbitrary h and p adaptivity. We prove the L2 stability for general solutions and give a detailed error estimate for smooth solutions, and provide numerical simulation results for different types of solutions of the nonlinear Camassa- Holm equation to illustrate the accuracy and capability of the LDG method.