线性有限元误差的L^2范数估计及其应用

The L^2 Norm Error Estimate for Linear Element and Its Applications

基于分片L^2投影的稳定性估计,证明了线性有限元误差和投影误差的等价性.进一步利用分片线性插值的误差展开式,得到了有限元L^2误差的一个误差估计子.结合提出的Hessian重构技术,构造了有限元L^2误差的一个后验误差估计子.数值算例说明了后验误差估计子的可靠性和有效性及相应自适应算法的数值表现.

In this paper,we prove that the error of linear finite element approximation and piecewise L^2 polynomial projection are equivelant by applying the stability estimation of the projection operator.Based on the error expansion of piecewise linear interpolation,we show that interpolation error can be used as an a posteriori error estimate that is both reliable and efficient.We further introduce a Hessian recovery technique and the corresponding recovery type a posteriori L^2 norm error estimation.Numerical examples are presented to show the efficiency of the a posteriori error estimator and the performance of the corresponding adaptive finite element method.