中文摘要：

一阶双曲问题的有限元后验误差估计至今没有得到很好的解决．本文对d维区域上一阶双曲问题的七次间断有限元逼近提出了一种新的后验误差分析方法，进而建立了间断有限元解在DG范数下（强于L2范数）基于误差余量型的后验误差估计．数值计算验证了本文理论分析的有效性．本文方法也适用于其他变分问题有限元逼近的后验误差分析．

英文摘要：

Until now, the a posteriori error estimates of finite element methods for first order hyperbolic problems are yet far from resolving well. In this paper, we propose a new a posteriori error analysis method for the discontinuous finite element approximates to first order hyperbolic problems in d space dimensions by using polynomials of order k, and then we establish efficiency residual-based a posteriori error estimates in the DG norm which is stronger then the L2 norm. The validity of our theoretical analysis is verified by some numerical experiments. Our method is also available for finite element approximations to other variational problems.