Volume 10, Issue 2
Convergent Adaptive Finite Element Method Based on Centroidal Voronoi Tessellations and Superconvergence

Yunqing Huang, Hengfeng Qin, Desheng Wang & Qiang Du

Commun. Comput. Phys., 10 (2011), pp. 339-370.

Published online: 2011-10

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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.

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@Article{CiCP-10-339, author = {Yunqing Huang, Hengfeng Qin, Desheng Wang and Qiang Du}, 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 = {

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.

}, issn = {1991-7120}, doi = {https://doi.org/10.4208/cicp.030210.051110a}, url = {http://global-sci.org/intro/article_detail/cicp/7445.html} }
TY - JOUR T1 - Convergent Adaptive Finite Element Method Based on Centroidal Voronoi Tessellations and Superconvergence AU - Yunqing Huang, Hengfeng Qin, Desheng Wang & Qiang Du JO - Communications in Computational Physics VL - 2 SP - 339 EP - 370 PY - 2011 DA - 2011/10 SN - 10 DO - http://dor.org/10.4208/cicp.030210.051110a UR - https://global-sci.org/intro/cicp/7445.html KW - AB -

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.

Yunqing Huang, Hengfeng Qin, Desheng Wang & Qiang Du. (1970). Convergent Adaptive Finite Element Method Based on Centroidal Voronoi Tessellations and Superconvergence. Communications in Computational Physics. 10 (2). 339-370. doi:10.4208/cicp.030210.051110a
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