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

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

2001-04-18

arxiv.org/abs/hep-th/0104151v1

Physics

High Energy Physics

High Energy Physics - Theory

15 pages, 3 figures

Scientific paper

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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