On Symplectic, Multisymplectic Structures-Preserving in Simple Finite Element Method

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By the simple finite element method, we study the symplectic, multisymplectic structures and relevant preserving properties in some semi-linear elliptic boundary value problem in one-dimensional and two-dimensional spaces respectively. We find that with uniform mesh, the numerical schemes derived from finite element method can keep a preserved symplectic structure in one-dimensional case and a preserved multisymplectic structure in two-dimentional case respectively. These results are in fact the intrinsic reason that the numerical experiments indicate that such finite element schemes are accurate in practice.
15 pages, 3 figures

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High Energy Physics - Theory

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http://salesiana.dossiersoluciones.com/handle/123456789/50641

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/hep-th/0104151
 http://arxiv.org/abs/hep-th/0104151

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arXiv