Local Discontinuous Galerkin Methods for the Two-Dimensional Camassa–Holm Equation Dedicated to Celebrate the Sixtieth Anniversary of USTC  

作　　者：Tian Ma Yan Xu 

机构地区：[1]School of Mathematical Sciences,University of Science and Technology of China,Hefei 230026,Anhui,People’s Republic of China

出　　处：《Communications in Mathematics and Statistics》2018年第3期359-388,共30页数学与统计通讯（英文）

基　　金：supported by NSFC Grant Nos.11722112,91630207.

摘　　要：In this paper,the local discontinuous Galerkin method is developed to solve the two-dimensional Camassa–Holm equation in rectangular meshes.The idea of LDG methods is to suitably rewrite a higher-order partial differential equations into a firstorder system,then apply the discontinuous Galerkin method to the system.A key ingredient for the success of such methods is the correct design of interface numerical fluxes.The energy stability for general solutions of the method is proved.Comparing with the Camassa–Holm equation in one-dimensional case,there are more auxiliary variables which are introduced to handle high-order derivative terms.The proof of the stability is more complicated.The resulting scheme is high-order accuracy and flexible for arbitrary h and p adaptivity.Different types of numerical simulations are provided to illustrate the accuracy and stability of the method.

关 键 词：Local discontinuous Galerkin method Two-dimensional Camassa-Holm equation Stability 

分 类 号：O17[理学—数学]