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中文摘要：
设计了一种基于显示多项式恢复（EPR）的后验误差估计,这种恢复是对函数值进行恢复,它的核心思想是在每条边上通过求解只有一个未知量的局部问题来恢复边中点的函数值。首先,给出了EPR方法的显示公式。该文基于EPR的后验误差估计分别与最新顶点加密方法和CVDT加密方法相结合,构造自适应有限元算法求解椭圆方程。数值试验表明基于EPR的后验误差是有效的,特别地对于泊松方程,在CVDT网格上EPR具有超收敛性质.最后,对一维情形,给出了相应的理论分析.
英文摘要：
This paper develops a posteriori error estimates based on a value recovery procedure called explicit polynomial recovery（EPR）.The key idea of this procedure is to recover the midpoint value by solving a local problem with one variable.First,we provide the explicit formulae for EPR.Then we considered two kinds of mesh adaptivity algorithms,one is the newest vertex bisection and the other is based on Centroidal Voronoi Delaunay Trianguation（CVDT）.Numerical experiments are presented to show that the new estimator is efficient,specifically for the EPR which has superconvergence on the CVDT meshes for the Poisson equations.Finally,some theoretical justifications are provided.
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