中文摘要：

通过数值试验发现Ainsworth建立的非协调Q^rot 1元可计算上界后误差估计指示子的可靠、有效性差．参照相关文献以及根据Q^rot 1元的性质，在Ainsworth建立的可计算上界后验误差估计框架下对插值后处理函数的构造和选取分别作了修改和更换，并相应获得可靠且有效的可计算上界后验误差估计，给出了三个不同类型的例子及其实验结果．

英文摘要：

This paper discovers the reliability and validity of the non-conforming rotated Q1 finite element computable upper bound a posteriori error estimate indicator established by M. Ainsworth are bad from the numerical experiments. Consulting the revelent paper and according to the property of the rotated Q1 element, this paper makes an modification for the construction of the interpolation post-processing and makes a replacement for the selection of the interpolation post-processing function under the framework established by M. Ainsworth, respectively, and obtains the reliable and effective computable upper bound a posteriori error estimates accordingly, and gives three different types of examples with experimental results.