中文摘要：

研究一类凹角区域双曲型外问题的数值方法．先用Newmark方法对时间进行离散化，在每个时间步求解一个椭圆外问题．然后引入人工边界，并获得精确的人工边界条件．给出半离散化问题的变分问题，证明了变分问题的适定性，并给出了误差估计．最后给出数值例子，以示该方法的可行性与有效性．

英文摘要：

The numerical method for the exterior hyperbolic problems with a concave angle domain is investigated. The governing equation is first discreted in time by Newmark method, leading to a time-stepping scheme, where an exterior elliptic problem has to be solved in each time step. Then an artificial boundary is introduced, an exact artificial boundary condition is obtained. The variational problem of semi-discrete problem is given, the well-posedness of the variational problem is proved, and some error estimates are presented. Finally, some numerical examples are presented to demonstrate the performance of the method.