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Open Access Research

Superconvergence patch recovery for the gradient of the tensor-product linear triangular prism element

Jinghong Liu1* and Yinsuo Jia2

Author Affiliations

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

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Boundary Value Problems 2014, 2014:1  doi:10.1186/1687-2770-2014-1

Published: 2 January 2014

Abstract

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 <a onClick="popup('http://www.boundaryvalueproblems.com/content/2014/1/1/mathml/M1','MathML',630,470);return false;" target="_blank" href="http://www.boundaryvalueproblems.com/content/2014/1/1/mathml/M1">View MathML</a> 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.

Keywords:
superconvergence patch recovery; superclose property; triangular prism element