A Local Discontinuous Galerkin Method for the Camassa-Holm Equation
TWENTE UNIV ENSCHEDE (NETHERLANDS)
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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.
- Numerical Mathematics