Conservative Discontinous Galerkin Method For The Camassa-Holm Equation

In this paper,we test a discontinous Galerkin method for solving the CamassaHolm equation which contains nonlinear high-order.We choice the proper flux to verify the energy conservation property of the Camassa-Holm equation.we also use the numerical examples to verify conservation property and Convergence.The first part introduces the background and research status and sources of the main structure of the article.Firstly,we introduced the development background and DG method equation. Then we introduces the discontinuous finite element method discrete numerical method on Camassa-Holm equation as well as some of the conclusions obtained.The second and third part of this paper analysis the semi-discrete and fully discrete of the Camassa-Holm equation.Under selecting the appropriate value of the flux,the format one will be conserved nature of the energy. Using Runge-Kutta method of the time-discrete give fully discrete.In the fourth part, we verify The accuracy and convergence, the fourth part of the article gives a detailed calculation, the test after a long numerical experiment testing methods to maintain the shape of the solution results.Numerical experiments confirm the stability and effectiveness of the proposed scheme.