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

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  • College of Mathematics and Computer Science, Hunan Normal University, Changsha 410081, P. R. China

Received date: 2010-10-18

  Revised date: 2011-04-11

  Online published: 2011-07-03

Supported by

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

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.

Cite this article

LI Can-Hua;CHEN Chuan-Miao . Ultraconvergence for averaging discontinuous finite elements and its applications in Hamiltonian system[J]. Applied Mathematics and Mechanics, 2011 , 32(7) : 943 -956 . DOI: 10.1007/s10483-011-1471-8

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