平均间断有限元的强超收敛性及在Hamilton系统的应用

讨论了常微分方程初值问题的k次平均间断有限元．当k为偶数时，证明了在节点上的平均通量（间断有限元在节点上的左右极限的平均值）有2k+2阶最佳强超收敛性．对具有动量守恒的非线性Hamilton系统(如Schrdinger方程和Kepler系统),发现此类间断有限元在节点上是动量守恒的．这些性质被数值试验所证实．

Ultraconvergence for Averaging Discontinuous Finite Elements and Its Applications in Hamiltonian System

The k-degree averaging discontinuous finite element solution for the initial value problem of ordinary differential equations was discussed. When k waseven, it was proved that the averaging numerical flux (the average of left and right lmiits for discon tinuous finite element at nodes) had the optmial order ultraconvergence 2k + 2. For non linear Hamiltonian systems (e. g., S chrêdinger equation and Kepler system) with momentum conservation, it was found that the discon tinuous finite element methods preserve momentum at nodes. These properties were confirmed by numerical expermients.