平均间断有限元的强超收敛性及在Hamilton系统的应用  

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

作　　者：李灿华[1] 陈传淼[1] 

机构地区：[1]湖南师范大学数学与计算机科学学院,长沙410081

出　　处：《应用数学和力学》2011年第7期883-894,共12页Applied Mathematics and Mechanics

基　　金：Project supported by the National Natural Science Foundation of China (No. 10771063)

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.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.

关 键 词：平均间断有限元 强超收敛 HAMILTON系统 动量守恒 

分 类 号：O242.21[理学—计算数学]