Volume 29, Issue 2
Finite Element Method with Superconvergence for Nonlinear Hamiltonian Systems

Chuanmiao Chen, Qiong Tang & Shufang Hu

J. Comp. Math., 29 (2011), pp. 167-184

Published online: 2011-04

Preview Full PDF 295 1932
Export citation
  • 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 long time.

  • Keywords

Nonlinear Hamiltonian systems Finiteelement method Superconvergence Energy conservation Symplecticity Trajectory

  • AMS Subject Headings

65N30.

  • Copyright

COPYRIGHT: © Global Science Press

  • Email address
  • BibTex
  • RIS
  • TXT
@Article{JCM-29-167, author = {Chuanmiao Chen, Qiong Tang and Shufang Hu}, title = {Finite Element Method with Superconvergence for Nonlinear Hamiltonian Systems}, journal = {Journal of Computational Mathematics}, year = {2011}, volume = {29}, number = {2}, pages = {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 long time.}, issn = {1991-7139}, doi = {https://doi.org/10.4208/jcm.1009-m3108}, url = {http://global-sci.org/intro/article_detail/jcm/8471.html} }
TY - JOUR T1 - Finite Element Method with Superconvergence for Nonlinear Hamiltonian Systems AU - Chuanmiao Chen, Qiong Tang & Shufang Hu JO - Journal of Computational Mathematics VL - 2 SP - 167 EP - 184 PY - 2011 DA - 2011/04 SN - 29 DO - http://doi.org/10.4208/jcm.1009-m3108 UR - https://global-sci.org/intro/article_detail/jcm/8471.html KW - Nonlinear Hamiltonian systems KW - Finiteelement method KW - Superconvergence KW - Energy conservation KW - Symplecticity KW - Trajectory AB - 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 long time.
Chuanmiao Chen, Qiong Tang & Shufang Hu. (1970). Finite Element Method with Superconvergence for Nonlinear Hamiltonian Systems. Journal of Computational Mathematics. 29 (2). 167-184. doi:10.4208/jcm.1009-m3108
Copy to clipboard
The citation has been copied to your clipboard