American Institute of Mathematical Sciences

March  2015, 20(2): 495-504. doi: 10.3934/dcdsb.2015.20.495

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

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

Received  August 2013 Revised  October 2014 Published  January 2015

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.
Citation: Jinghong Liu, Yinsuo Jia. Gradient superconvergence post-processing of the tensor-product quadratic pentahedral finite element. Discrete & Continuous Dynamical Systems - B, 2015, 20 (2) : 495-504. doi: 10.3934/dcdsb.2015.20.495
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