有限元后验误差估计的有效性分析

本文利用第二类方法──局部求解法，对一般区域和正规网格上高次三角形元和矩形元，构造并分析了一种等价后验误差估计量．同时，给出了等价上、下界的计算公式和估计式．分析结果表明：上、下界强烈依赖于网格的几何特性，而与原方程解的光滑性关系较弱．

ANALYSIS OF THE EFFICIENCY OF AN A-POSTERIORI ERROR ESTIMATOR FOR FINITE ELEMENTS

I construct and analyze a type of equivalent a-posteriori error estimators,using the second kind of method, namely: local solving method, for higher tritngular and quadrangular finite elements in general domain and regular meshes. In addifion, it is showed that up bound and down bound depend strongly on the geometry of elements,but they have weaker relation with the smoothness of the solution of original equation.