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

Han-Ying Guo·Xiao-mei Ji·Yu-Qi Li·Ke Wu
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Abstract

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.

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Han-Ying Guo, Xiao-mei Ji, Yu-Qi Li, Ke Wu. 2001-04-18. On Symplectic, Multisymplectic Structures-Preserving in Simple Finite Element Method. https://arxiv.org/abs/hep-th/0104151

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