Superconvergence patch recovery for the gradient of the tensor-product linear triangular prism element
1 Department of Fundamental Courses, Ningbo Institute of Technology, Zhejiang University, Qianhu South Road, Ningbo, China
2 School of Mathematics and Computer Science, Shangrao Normal University, Zhimin Road, Shangrao, 334001, China
Boundary Value Problems 2014, 2014:1 doi:10.1186/1687-2770-2014-1Published: 2 January 2014
In this article, we study superconvergence of the finite element approximation to the solution of a general second-order elliptic boundary value problem in three dimensions over a fully uniform mesh of piecewise tensor-product linear triangular prism elements. First, we give the superclose property of the gradient between the finite element solution and the interpolant Πu. Second, we introduce a superconvergence recovery scheme for the gradient of the finite element solution. Finally, superconvergence of the recovered gradient is derived.