EFFICIENT ADAPTIVE FINITE ELEMENT METHOD BASED ON CENTROIDAL VORONOI TESSELLATIONS AND SUPERCONVERGENCE
主 题: EFFICIENT ADAPTIVE FINITE ELEMENT METHOD BASED ON CENTROIDAL VORONOI TESSELLATIONS AND SUPERCONVERGENCE
报告人: 黄云清 教授 (湘潭大学)
时 间: 2010-01-22 14:00 - 15:00
地 点: 理科一号楼 1114(数学所活动)
We present a novel adaptive ?nite element method (AFEM) for elliptic equations which is based upon 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 ?nite element solutions on such high quality
triangulations, superconvergent recovery methods become particularly e?ective so that asymptotically exact a posteriori error estimations can be obtained. Through a seamless integration of these techniques, a convergent adaptation 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.
