A LOCAL DISCONTINUOUS GALERKIN METHOD FOR THECAMASSA-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 L~2 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.