线弹性有限元的自适应加密与多重网格法求解

Adaptive Refinement and Multigrid Solution for Linear Finite Element Method

基于Ｚｉｅｎｋｉｅｗｉｃｚ－Ｚｈｕ误差估计方法、自适应策略以及分子表结构，研制出功能强大的自适应多重网格有限元程序．该程序可对任意曲线组成的计算区域进行全局与局部加密，以应力集中问题为例，展示了自适应多重网格有限元的主要特征．研究结果表明：本文采用的误差估计方法、自适应策略对线弹性问题是有效的．自适应多重网格有限元求解应力集中问题具有精度高、收敛速度快的优点．

ased on Zienkiewicz-Zhu error estimation,adaptive refinement strategy and molecular list data strcture,an adaptive multigrid FEM program with powerful functions is developed in this paper.The program can refine the region composed of any curves adaptively. The main characteristics of the adaptive multigrid FEM can be illustrated by the problem of stress con- centration. The results demonstrate that the error estimation and refinement strategy used in this peper are effective for linear elastic problems. The adaptive multigrid FEM has the ad- vantages of high accuracy and fast rate of convergence in solving stress concentration prob- lems.