LONG-TIME PROPERTIES OF FINITE ELEMENTS FOR HAMILTONIAN SYSTEM AND THE PROOF OF FENG'S CONJECTU

• 作 者: CHUANMIAOCHEN;
• 机 构: HUNAN NORMAL UNIVERSITY
• 出 处: 第三届国际微分方程的数值分析会议(3rd International Conference on Numerical A
• 发表日期: 2013年期

　　Symplectic algorithms and finite element methods(FEM) for Hamiltonian system are summarized,and three conjectures on long-time deviations of computational orbit,energy and symplecticity are proposed.This paper emphasizes the continuous nite element method and its energy conservation,proposes the basic assumption A on H(z) and derives three uniform bounds.It is proved that long-time deviation of nite element orbit grows linearly with time(Fengs conjecture),based on superconvergence result for short time and a new approach.Numerical experiments verify the validity of three conjectures.