中文摘要：

这篇论文为横梁问题为有限元素方法建议一个可靠、有效的后验错误评估者。错误能被可计算出来的错误评估者从上面并且下面围住直到也也不不在横梁的厚度上取决于网孔尺寸的趋于增加的常数，这被证明。

英文摘要：

This paper proposes a reliable and efficient a posteriori error estimator for the finite element methods for the beam problem. It is proved that the error can be bounded by the computable error estimator from above and below up to multiplicative constants that do neither depend on the meshsize nor on the thickness of the beam.