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Convergent Adaptive Finite Element Method Based on Centroidal Voronoi Tessellations and Superconvergence

Published online by Cambridge University Press:  20 August 2015

Yunqing Huang ,
Hengfeng Qin ,
Desheng Wang  and
Qiang Du
Yunqing Huang*
Affiliation:
Hunan Key Laboratory for Computation and Simulation in Science and Engineering, Xiangtan University, Hunan 411105, China
Hengfeng Qin*
Affiliation:
Department of Mechanical and Electronic Engineering, School of Mechanical Engineering, Xiangtan University, Hunan 411105, China
Desheng Wang*
Affiliation:
Division of Mathematical Sciences, School of Physical and Mathematical Sciences, Nanyang Technological University, Singapore 637371, Singapore
Qiang Du*
Affiliation:
Department of Mathematics, Pennsylvania State University, University Park, PA 16802, USA
*
Corresponding author.Email:huangyq@xtu.edu.cn
Email:qinhf2001@yahoo.com.cn
Email:desheng@ntu.edu.sg
Email:qdu@math.psu.edu
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Abstract

We present a novel adaptive finite element method (AFEM) for elliptic equations which is based upon the Centroidal Voronoi Tessellation (CVT) and superconvergent gradient recovery. The constructions of CVT and its dual Centroidal Voronoi Delaunay Triangulation (CVDT) are facilitated by a localized Lloyd iteration to produce almost equilateral two dimensional meshes. Working with finite element solutions on such high quality triangulations, superconvergent recovery methods become particularly effective so that asymptotically exact a posteriori error estimations can be obtained. Through a seamless integration of these techniques, a convergent adaptive procedure is developed. As demonstrated by the numerical examples, the new AFEM is capable of solving a variety of model problems and has great potential in practical applications.

Keywords

65N5065N15Finite element methodssuperconvergent gradient recoveryCentroidal Voronoi Tessellationadaptive methods
Type
Research Article
Information
Communications in Computational Physics , Volume 10 , Issue 2 , August 2011 , pp. 339 - 370
Copyright
Copyright © Global Science Press Limited 2011

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