Ultraconvergence for averaging discontinuous finite elements and its applications in Hamiltonian system  

作　　者：李灿华 陈传森 

机构地区：[1]College of Mathematics and Computer Science,Hunan Normal University

出　　处：《Applied Mathematics and Mechanics(English Edition)》2011年第7期943-956,共14页应用数学和力学（英文版）

基　　金：Project supported by the National Natural Science Foundation of China (No. 10771063)

摘　　要：This paper discusses the k-degree averaging discontinuous finite element solution for the initial value problem of ordinary differential equations. When k is even, the averaging numerical flux （the average of left and right limits for the discontinuous finite element at nodes） has the optimal-order ultraconvergence 2k ＋ 2. For nanlinear Hamiltonian systems （e.g., SchrSdinger equation and Kepler system） with momentum conservation, the discontinuous finite element methods preserve momentum at nodes. These properties are confirmed by numerical experiments.This paper discusses the k-degree averaging discontinuous finite element solution for the initial value problem of ordinary differential equations. When k is even, the averaging numerical flux （the average of left and right limits for the discontinuous finite element at nodes） has the optimal-order ultraconvergence 2k ＋ 2. For nanlinear Hamiltonian systems （e.g., SchrSdinger equation and Kepler system） with momentum conservation, the discontinuous finite element methods preserve momentum at nodes. These properties are confirmed by numerical experiments.

关 键 词：averaging discontinuous finite element ULTRACONVERGENCE Hamiltoniansystem momentum conservation 

分 类 号：O241.82[理学—计算数学]