【摘要】 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.更多还原

【Abstract】 The k-degree averaging discontinuous finite element solution for the initial value problem of ordinary differential equations was discussed.When k was even,it was proved that the averaging numerical flux(the average of left and right limits for discontinuous finite element at nodes) had the optimal order ultraconvergence 2k+2.For nonlinear Hamiltonian systems(e.g.,Schrdinger equation and Kepler system) with momentum conservation,it was found that the discontinuous finite element methods preserve momentum at nodes.These properties were confirmed by numerical experiments.更多还原