基于三角形剖分的最小二乘混合元超收敛性研究

Superconvergence of Least-Squares Mixed Finite Elements for Elliptic Problems on Triangulation

讨论了二阶椭圆问题的最小二乘混合元方法及其超收敛性 ,采用一致三角形剖分、分片一次多项式空间对未知函数作有限元逼近 ,而对其通量则采用最低阶的Raviart -Thomas元逼近 ,通过投影算子和辅助算子的技术 ,得到了精度为O(h3 2 )

In this paper, a superconvergence result is derived by the least squares mixed finite elements method for the second order elliptic equations on triangulation. These estimates are based on projection operators and an auxiliary projection and when lowest order triangular mixed finite elements of Raviart-Thomas type on regular families of uniform triangulations are used we can obtain superconvergence estimates of both the primary solution approximation u h  and the flux approximation p h with the accuracy of O(h 3/2 ).