Continuous finite element methods for Hamiltonian systems  

作　　者：汤琼 陈传淼 

机构地区：[1]College of Mathematics and Computer Science Hunan Normal University,Changsha 410081,P.R.China Department of Information and Computing Science,Hunan University of Technology,Zhuzhou 412008,Hunan Province,P.R.China [2]College of Mathematics and Computer Science Hunan Normal University,Changsha 410081,P.R.China

出　　处：《Applied Mathematics and Mechanics(English Edition)》2007年第8期1071-1080,共10页应用数学和力学（英文版）

基　　金：Project supported by the National Natural Science Foundation of China (No.10471038)

摘　　要：By applying the continuous finite element methods of ordinary differential equations, the linear element methods are proved having second-order pseudo-symplectic scheme and the quadratic element methods are proved having third-order pseudo- symplectic scheme respectively for general Hamiltonian systems, and they both keep energy conservative. The finite element methods are proved to be symplectic as well as energy conservative for linear Hamiltonian systems. The numerical results are in agree-ment with theory.By applying the continuous finite element methods of ordinary differential equations, the linear element methods are proved having second-order pseudo-symplectic scheme and the quadratic element methods are proved having third-order pseudo- symplectic scheme respectively for general Hamiltonian systems, and they both keep energy conservative. The finite element methods are proved to be symplectic as well as energy conservative for linear Hamiltonian systems. The numerical results are in agree-ment with theory.

关 键 词：Hamiltonian systems continuous finite element methods pseudo-symplectic energy conservation 

分 类 号：O242.21[理学—计算数学]