Betsch, P. and Steinmann, P. (2000) Conservation properties of a time FE method. Part I: time-stepping schemes for N-body problems. International Journal for Numerical Methods in Engineering, 49(5), pp. 599-638. (doi: 10.1002/1097-0207(20001020)49:5<599::AID-NME960>3.0.CO;2-9)
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Abstract
In the present paper one‐step implicit integration algorithms for the N‐body problem are developed. The time‐stepping schemes are based on a Petrov–Galerkin finite element method applied to the Hamiltonian formulation of the N‐body problem. The approach furnishes algorithmic energy conservation in a natural way. The proposed time finite element method facilitates a systematic implementation of a family of time‐stepping schemes. A particular algorithm is specified by the associated quadrature rule employed for the evaluation of time integrals. The influence of various standard as well as non‐standard quadrature formulas on algorithmic energy conservation and conservation of angular momentum is examined in detail for linear and quadratic time elements.
| Item Type: | Articles |
|---|---|
| Status: | Published |
| Refereed: | Yes |
| Glasgow Author(s) Enlighten ID: | Steinmann, Professor Paul |
| Authors: | Betsch, P., and Steinmann, P. |
| College/School: | College of Science and Engineering > School of Engineering > Infrastructure and Environment |
| Journal Name: | International Journal for Numerical Methods in Engineering |
| Publisher: | Wiley |
| ISSN: | 0029-5981 |
| ISSN (Online): | 1097-0207 |
| Published Online: | 29 August 2000 |
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