Gradient superconvergence post-processing of the tensor-product quadratic pentahedral finite element

Jinghong Liu; Yinsuo Jia

doi:10.3934/dcdsb.2015.20.495

Article Contents

2015, Volume 20, Issue 2: 495-504. Doi: 10.3934/dcdsb.2015.20.495

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Gradient superconvergence post-processing of the tensor-product quadratic pentahedral finite element

Jinghong Liu^1, and
Yinsuo Jia^2,

1.
Department of Fundamental Courses, Ningbo Institute of Technology, Zhejiang University, Ningbo, 315100
2.
School of Mathematics and Computer Science, Shangrao Normal University, Shangrao, 334001

Received: July 31, 2013

Revised: September 30, 2014

Published: February 2015

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Abstract

In this article, using the well-known Superconvergent Patch Recovery (SPR) method, we present a gradient superconvergence post-processing scheme for the tensor-product quadratic pentahedral finite element approximation to the solution of a general second-order elliptic boundary value problem in three dimensions over fully uniform meshes. The supercloseness property of the gradients between the finite element solution $u_h$ and the tensor-product quadratic interpolation $\Pi u$ is first given. Then we show that the gradient recovered from the finite element solution by using the SPR method is superconvergent to $\nabla u$ at interior vertices.

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Mathematics Subject Classification: Primary: 65N30; Secondary: 65N12.

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