一个高效的一维有限元自适应求解的新方案 第十三届全国结构工程学术大会特邀报告

AN EFFICIENT SELF-ADAPTIVE STRATEGY FOR ONE-DIMENSIONAL FINITE ELEMENT METHOD

基于新近提出的一维有限元后处理超收敛算法——单元能量投影(EEP)法,将有限元自适应求解问题转化为对超收敛解答的自适应分段多项式插值问题,一步便可获得最优的有限元网格划分,在该网格上再次进行有限元计算,即可获得满足用户给定的误差限的有限元解答。该法简单实用、快速高效,是一个颇具优势和潜力的自适应方法。文中以二阶常微分方程模型问题为例,对该法的形成思路和实施策略做一介绍,并给出有代表性的数值算例用以展示该法的优良性能和效果。

Based on the newly-developed Element Energy Projection (EEP) method for computation of super-convergent results in one-dimensional Finite Element Method (FEM), the task of self-adaptive FEM analysis is converted into the task of adaptive piecewise polynomial interpolation. As a result, an optimum FEM mesh can be obtained, and further FEM analysis on this mesh would immediately produce a FEM solution which satisfies the user specified error tolerance. This strategy has been found to be very simple, rapid, ch...