Applied Mathematics and Mechanics (English Edition) ›› 2011, Vol. 32 ›› Issue (7): 943-956.doi: https://doi.org/10.1007/s10483-011-1471-8

• Articles • 上一篇    

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

李灿华 陈传淼     

  1. College of Mathematics and Computer Science, Hunan Normal University, Changsha 410081, P. R. China
  • 收稿日期:2010-10-18 修回日期:2011-04-11 出版日期:2011-07-03 发布日期:2011-07-03
  • 基金资助:

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

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

 LI Can-Hua, CHEN Chuan-Miao     

  1. College of Mathematics and Computer Science, Hunan Normal University, Changsha 410081, P. R. China
  • Received:2010-10-18 Revised:2011-04-11 Online:2011-07-03 Published:2011-07-03
  • Supported by:

    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 nonlinear Hamiltonian systems (e.g., Schr¨odinger equation and Kepler system) with momentum conservation, the discontinuous finite element methods preserve momentum at nodes. These properties are confirmed by numerical experiments.

Abstract: 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 nonlinear Hamiltonian systems (e.g., Schr¨odinger equation and Kepler system) with momentum conservation, the discontinuous finite element methods preserve momentum at nodes. These properties are confirmed by numerical experiments.

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