Research Article

Centroidal Voronoi tessellation-based finite element superconvergence

  1. Yunqing Huang1,
  2. Hengfeng Qin2,
  3. Desheng Wang3,*

Article first published online: 10 JUL 2008

DOI: 10.1002/nme.2374

Issue

International Journal for Numerical Methods in Engineering

International Journal for Numerical Methods in Engineering

Volume 76, Issue 12, pages 1819–1839, 17 December 2008

Additional Information

How to Cite

Huang, Y., Qin, H. and Wang, D. (2008), Centroidal Voronoi tessellation-based finite element superconvergence. International Journal for Numerical Methods in Engineering, 76: 1819–1839. doi: 10.1002/nme.2374

Author Information

  1. 1

    Hunan Key Laboratory for Computation and Simulation in Science and Engineering, Xiangtan University, Hunan, People's Republic of China

  2. 2

    Department of Mathematics, Xiangtan University, Hunan, People's Republic of China

  3. 3

    Division of Mathematical Sciences, School of Physical and Mathematical Sciences, Nanyang Technological University, Singapore 637616, Singapore

*Division of Mathematical Sciences, School of Physical and Mathematical Sciences, Nanyang Technological University, 1 Nanyang Walk, Block 5, Level 3, Singapore 637616, Singapore

Publication History

  1. Issue published online: 19 NOV 2008
  2. Article first published online: 10 JUL 2008
  3. Manuscript Accepted: 31 MAR 2008
  4. Manuscript Revised: 10 MAR 2008
  5. Manuscript Received: 15 OCT 2007

Funded by

  • NSFC for Distinguished Young Scholars. Grant Number: 10625106
  • National Basic Research Program of China. Grant Number: 2005CB321701
  • Nanyang Technological University Start-up Grant. Grant Number: M58110011

SEARCH

SEARCH BY CITATION

ARTICLE TOOLS

Get PDF (2020K)

Keywords:

  • finite element methods;
  • superconvergence;
  • centroidal Voronoi tessellation;
  • Delaunay triangulation

Abstract

In this article, a finding on finite element superconvergence is reported. The Laplacian operator with Dirichlet boundary condition is considered. The linear finite element solutions have an O(h2+α)(α≈0.5)-superconvergence in l2 norm at nodes on an almost equilateral triangular mesh generated based on centroidal Voronoi tessellation, for an arbitrary 2D bounded domain. Extensive numerical examples are presented to demonstrate the superconvergence property. Copyright © 2008 John Wiley & Sons, Ltd.

Get PDF (2020K)