Lagrange三次有限体积元法的超收敛现象  

Superconvergence Phenomenon for Lagrange Cubic Finite Volume Element Method

作　　者：丁玉琼[1] 左平[2] 

机构地区：[1]吉林大学数学研究所,长春130012 [2]空军航空大学基础部,长春130022

出　　处：《吉林大学学报（理学版）》2011年第2期159-163,共5页Journal of Jilin University:Science Edition

基　　金：国家自然科学基金(批准号:10971082)

摘　　要：基于三角形网上求解Poisson方程的Lagrange三次有限体积元法,给出了超收敛性的数值结果.数值实验表明,在三角形单元的对称点(即3边中点和3个角顶点)上,数值解平均梯度的收敛阶约为4阶,比按H1模的收敛阶(O(h3))约高一阶.Based on the Lagrangian cubic element finite volume method for Poisson equation on triangular meshes constructed by us,we found that the convergence rate of average gradient of the numerical solutions is approximately 4 order at the symmetrical points of triangular element（i.e.midpoints of three edges and three vertices） through the numerical experiments,which is nearly one order higher than that of the H1 norm（O（h3））.

关 键 词：有限体积元法 Lagrange三次元 对偶剖分 超收敛 

分 类 号：O241.82[理学—计算数学]