| All along,the Korteweg-de Vries(Kd V)equation occupies an important position in the partial differential equation.It can be used to describe many physical phenomena,and has an infinite number of the conservation law,which makes it widely used in various subject areas.Therefore,it is very meaningful to find an effective and stable numerical method to solve the equation and maintain the conservative nature of the original problem.Discontinuous Galerkin(DG)finite element method is an accurate and effective numerical method.Not only can high-order precision approximations of smooth solutions be obtained,but also complex solution areas can be handled well.This dissertation uses two DG methods to solve the Kd V equation,namely the energy conservation DG method and the local discontinuous Galerkin(LDG)method.What these two methods have in common is that they need to introduce auxiliary variables or functions,and rewrite the original equations into equations to solve.The difference is that the LDG method transforms the higher-order problems into first-order problems,but the energy conservation DG method does not require.When using the DG method to solve a problem,the choice of flux is very important,especially in the analysis of energy conservation and error estimation.Because this article wants to get the conclusion of conservation of energy,the conservative numerical flux is chosen.The format of its construction makes these two methods can maintain the characteristics of energy conservation.In this dissertation,when using these two methods to solve the Kd V equation,the corresponding numerical scheme is constructed,and the energy conservation analysis of the format and the error estimation between the numerical solution and the exact solution are studied.Finally,three numerical examples are given,and these examples and formats are programmed with MATLAB.The results obtained well verify the conclusions obtained in the article and prove the validity of the conclusions. |
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