@Article{CiCP-10-2,
author = {},
title = {Convergent Adaptive Finite Element Method Based on Centroidal Voronoi Tessellations and Superconvergence},
journal = {Communications in Computational Physics},
year = {2011},
volume = {10},
number = {2},
pages = {339--370},
abstract = {<p style="text-align: justify;">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.</p>},
issn = {1991-7120},
doi = {https://doi.org/10.4208/cicp.030210.051110a},
url = {https://global-sci.com/article/80925/convergent-adaptive-finite-element-method-based-on-centroidal-voronoi-tessellations-and-superconvergence}
}