CAJ | 학술논문

讨论非线性常微分方程初值问题偶次平均间断有限元的强超收敛性．用对偶论证和简化的连续性方法证明，偶次（k=0，2，4，…）间断元的节点流通量Uj（U^-j＋U^＋j）／2有最高阶超收敛O（h^2k＋2）；用数值例子证实了此超收敛阶，误差图表明单元内部还有超收敛点．
토론비선성상미분방정초치문제우차평균간단유한원적강초수렴성．용대우론증화간화적련속성방법증명，우차（k=0，2，4，…）간단원적절점류통량Uj（U^-j＋U^＋j）／2유최고계초수렴O（h^2k＋2）；용수치례자증실료차초수렴계，오차도표명단원내부환유초수렴점．
Uttraconvergence of the even degree averaging discontinuous finite elements for nonlinear ordinary differential equations with initial value is discussed. Using dual argument and simplified continuation method, the highest order superconvergenee O(h2k+2) of the numerical flux Uj = (U^-j+U^+j )/2 at nodes for even degree (such as k=0,2,4,...) discontinuous finite elements is proved. The highest order is confirmed by our nurneri cal experiments and error figures also show that there are superconvergent points in elements.