哈密尔顿系统的连续有限元法及守恒性

Continuous finite element methods of Hamilton systems and conservation

利用常微分方程的连续有限元法,证明了线性哈密尔顿系统的连续一、二、三次有限元法为辛算法;对非线性哈密尔顿系统,本文证明了连续一次有限元在3阶量意义下近似保辛,且保持能量守恒,并在数值计算上探讨了守恒性和近似程度,结果与理论相吻合。

By applying the continuous finite element methods for ordinary differential equations, the first, second and third order finite element methods for linear Hamiltonian systems are proved to be symplectie as well as energy conservative. In addition, the linear element for nonlinear Hamiltonian systems are approximately sympleetic on three order accuracy meaning, while they remain energy conservation. The numerical results are in agreement with theory.