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Korean Mathematical Society JKMS

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J. Korean Math. Soc. 2016; 53(6): 1411-1429

Online first article August 25, 2016      Printed November 1, 2016

https://doi.org/10.4134/JKMS.j150547

Copyright © The Korean Mathematical Society.

The gradient recovery for finite volume element method on quadrilateral meshes

Yingwei Song and Tie Zhang

Northeastern University, Northeastern University

Abstract

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We consider the finite volume element method for elliptic problems using isoparametric bilinear elements on quadrilateral meshes. A gradient recovery method is presented by using the patch interpolation technique. Based on some superclose estimates, we prove that the recovered gradient $R(\nabla u_h)$ possesses the superconvergence: $\|\nabla u-R(\nabla u_h)\|=O(h^2)\|u\|_3$. Finally, some numerical examples are provided to illustrate our theoretical analysis.

Keywords: finite volume method, elliptic problem, quadrilateral meshes, gradient recovery, superconvergence

MSC numbers: Primary 65N15, 65N30, 65M60

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