Centroidal Voronoi tessellation‐based finite element superconvergence

Abstract

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 ( h 2+α )(α≈0.5)‐superconvergence in l 2 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.