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IMA Journal of Numerical Analysis Advance Access originally published online on October 29, 2008
IMA Journal of Numerical Analysis 2009 29(4):1008-1022; doi:10.1093/imanum/drn050
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© The author 2008. Published by Oxford University Press on behalf of the Institute of Mathematics and its Applications. All rights reserved.

Enhancing eigenvalue approximation by gradient recovery on adaptive meshes

Haijun Wu{dagger}

Department of Mathematics, Nanjing University, Jiangsu 210093, People's Republic of China

Zhimin Zhang{ddagger}

Department of Mathematics, Wayne State University, Detroit, MI 48202, USA

{dagger} Corresponding author. Email: hjw{at}nju.edu.cn

{ddagger} Email: ag7761{at}wayne.edu

Received on 16 September 2007. Revised on 14 June 2008.


  Abstract

We utilize the recovered gradient by the polynomial-preserving recovery to enhance the eigenvalue approximation of the Laplace operator under adaptive meshes. Superconvergence rate is established and numerical tests on benchmark problems support our theoretical findings.

Key Words: adaptive finite-element method; eigenvalue; superconvergence; gradient recovery


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