Study of Finite Elements for Hamilton Systems
Hamilton系统的有限元研究

Two nice properties of the continuous finite element method for Hamilton systems are proved as follows: in any case the m-degree finite elements always preserve the energy which is sympletic for linear systems and is approximately sympletic with high accuracy O(h2m+1) in each stepping for nonlinear systems. In long-time computation the deviation of trajectories and their periods in time-space plane will crease linearly with time. Numerical experiments show that their deviations are often smaller than that of other schemes.