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The Gradient Superconvergence of Bilinear Finite Volume Element for Elliptic Problems

Part of:Partial differential equations, boundary value problemsPartial differential equations, initial value and time-dependent initial-boundary value problems

Published online by Cambridge University Press:  17 November 2016

Tie Zhang and
Lixin Tang
Tie Zhang*
Affiliation:
Department of Mathematics and the State Key Laboratory of Synthetical Automation for Process Industries, Northeastern University, Shenyang 110004, China
Lixin Tang*
Affiliation:
Department of Mathematics and the State Key Laboratory of Synthetical Automation for Process Industries, Northeastern University, Shenyang 110004, China
*
*Corresponding author. Email addresses:ztmath@163.com (T. Zhang), lixintang@mail.neu.edu.cn (L.-X. Tang)
*Corresponding author. Email addresses:ztmath@163.com (T. Zhang), lixintang@mail.neu.edu.cn (L.-X. Tang)

Abstract

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We study the gradient superconvergence of bilinear finite volume element (FVE) solving the elliptic problems. First, a superclose weak estimate is established for the bilinear form of the FVE method. Then, we prove that the gradient approximation of the FVE solution has the superconvergence property:

where denotes the average gradient on elements containing point P and S is the set of optimal stress points composed of the mesh points, the midpoints of edges and the centers of elements.

Keywords

Bilinear finite volume elementelliptic problemgradient approximationsuperconvergence

MSC classification

Secondary:65N30: Finite elements, Rayleigh-Ritz and Galerkin methods, finite methods65M60: Finite elements, Rayleigh-Ritz and Galerkin methods, finite methods

Information

Type
Research Article
Information
Numerical Mathematics: Theory, Methods and Applications , Volume 9 , Issue 4 , November 2016, pp. 579 - 594
Copyright
Copyright © Global-Science Press 2016 

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