Hamilton系统的连续有限元法

Continuous Finite Element Methods of Hamilton Systems

利用常微分方程的连续有限元法,对非线性Hamilton系统证明了连续一次、二次有限元法分别是2阶和3阶的拟辛格式,且保持能量守恒;连续有限元法是辛算法对线性Hamilton系统,且保持能量守恒.在数值计算上探讨了辛性质和能量守恒性,与已有的辛算法进行对比,结果与理论相吻合.

By applying the continuous finite element methods of ordinary differential equations, the linear dement methods are proved have pseudo-symplectic scheme of order 2 and the quadratic element methods have pseudo-symplectic scheme of order 3 respectively for general Hamiltonian systems, as well as energy conservative. The finite element raethods are proved to be symplectic as well as energy conservative for linear Hamiltonian systems. The numerical results are in agreement with theory.