Year: 2011
Journal of Computational Mathematics, Vol. 29 (2011), Iss. 2 : pp. 167–184
Abstract
This paper is concerned with the finite element method for nonlinear Hamiltonian systems from three aspects: conservation of energy, symplicity, and the global error. To study the symplecticity of the finite element methods, we use an analytical method rather than the commonly used algebraic method. We prove optimal order of convergence at the nodes $t_n$ for mid-long time and demonstrate the symplecticity of high accuracy. The proofs depend strongly on superconvergence analysis. Numerical experiments show that the proposed method can preserve the energy very well and also can make the global trajectory error small for a long time.
You do not have full access to this article.
Already a Subscriber? Sign in as an individual or via your institution
Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/jcm.1009-m3108
Journal of Computational Mathematics, Vol. 29 (2011), Iss. 2 : pp. 167–184
Published online: 2011-01
AMS Subject Headings:
Copyright: COPYRIGHT: © Global Science Press
Pages: 18
Keywords: Nonlinear Hamiltonian systems Finite element method Superconvergence Energy conservation Symplecticity Trajectory.
-
Runge-kutta method, finite element method, and regular algorithms for hamiltonian system
Hu, Shu-fang | Chen, Chuan-miaoApplied Mathematics and Mechanics, Vol. 34 (2013), Iss. 6 P.747
https://doi.org/10.1007/s10483-013-1704-8 [Citations: 2] -
Ultraconvergence for averaging discontinuous finite elements and its applications in Hamiltonian system
Li, Can-hua | Chen, Chuan-miaoApplied Mathematics and Mechanics, Vol. 32 (2011), Iss. 7 P.943
https://doi.org/10.1007/s10483-011-1471-8 [Citations: 1] -
Generating Function Methods for Coefficient-Varying Generalized Hamiltonian Systems
Li, Xueyang | Xiao, Aiguo | Wang, DonglingAdvances in Applied Mathematics and Mechanics, Vol. 6 (2014), Iss. 01 P.87
https://doi.org/10.4208/aamm.12-m12112 [Citations: 0] -
RIGOROUS DERIVATION OF HAMILTONIAN FROM LAGRANGIAN FOR SOLID CONTINUUM
HORI, Muneo | WIJERATHNE, Lalith | RIAZ, Rizwan | ICHIMURA, TsuyoshiJournal of JSCE, Vol. 6 (2018), Iss. 1 P.1
https://doi.org/10.2208/journalofjsce.6.1_1 [Citations: 1]