Combined with the characteristics of separable Hamiltonian systems and the finite element methods of ordinary differential equations, we prove that the composition of linear, quadratic, cubic finite element methods are symplectic integrator to separable Hamiltonian systems, i.e. the symplectic condition is preserved exactly, but the energy is only approximately conservative after compound. These conclusions are confirmed by our numerical experiments.
| Published in | Applied and Computational Mathematics (Volume 4, Issue 2) |
| DOI | 10.11648/j.acm.20150402.12 |
| Page(s) | 39-46 |
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This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited. |
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Copyright © The Author(s), 2024. Published by Science Publishing Group |
Separable Hamiltonian Systems, Finite Element Methods, Composition Methods, Symplectic Integrator
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APA Style
Qiong Tang, Luohua Liua, Yujun Zheng. (2015). The Continuous Finite Element Methods for a Simple Case of Separable Hamiltonian Systems. Applied and Computational Mathematics, 4(2), 39-46. https://doi.org/10.11648/j.acm.20150402.12
ACS Style
Qiong Tang; Luohua Liua; Yujun Zheng. The Continuous Finite Element Methods for a Simple Case of Separable Hamiltonian Systems. Appl. Comput. Math. 2015, 4(2), 39-46. doi: 10.11648/j.acm.20150402.12
AMA Style
Qiong Tang, Luohua Liua, Yujun Zheng. The Continuous Finite Element Methods for a Simple Case of Separable Hamiltonian Systems. Appl Comput Math. 2015;4(2):39-46. doi: 10.11648/j.acm.20150402.12
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Download@article{10.11648/j.acm.20150402.12,
author = {Qiong Tang and Luohua Liua and Yujun Zheng},
title = {The Continuous Finite Element Methods for a Simple Case of Separable Hamiltonian Systems},
journal = {Applied and Computational Mathematics},
volume = {4},
number = {2},
pages = {39-46},
doi = {10.11648/j.acm.20150402.12},
url = {https://doi.org/10.11648/j.acm.20150402.12},
eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.acm.20150402.12},
abstract = {Combined with the characteristics of separable Hamiltonian systems and the finite element methods of ordinary differential equations, we prove that the composition of linear, quadratic, cubic finite element methods are symplectic integrator to separable Hamiltonian systems, i.e. the symplectic condition is preserved exactly, but the energy is only approximately conservative after compound. These conclusions are confirmed by our numerical experiments.},
year = {2015}
}
TY - JOUR T1 - The Continuous Finite Element Methods for a Simple Case of Separable Hamiltonian Systems AU - Qiong Tang AU - Luohua Liua AU - Yujun Zheng Y1 - 2015/03/06 PY - 2015 N1 - https://doi.org/10.11648/j.acm.20150402.12 DO - 10.11648/j.acm.20150402.12 T2 - Applied and Computational Mathematics JF - Applied and Computational Mathematics JO - Applied and Computational Mathematics SP - 39 EP - 46 PB - Science Publishing Group SN - 2328-5613 UR - https://doi.org/10.11648/j.acm.20150402.12 AB - Combined with the characteristics of separable Hamiltonian systems and the finite element methods of ordinary differential equations, we prove that the composition of linear, quadratic, cubic finite element methods are symplectic integrator to separable Hamiltonian systems, i.e. the symplectic condition is preserved exactly, but the energy is only approximately conservative after compound. These conclusions are confirmed by our numerical experiments. VL - 4 IS - 2 ER -
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