The solution to the elastodynamic equation in the exterior of a polyhedral domain or a screen exhibits singular behavior from the corners and edges. The detailed expansion of the singularities implies quasi-optimal estimates for piecewise polynomial approximations of the Dirichlet trace of the solution and the traction. The results are applied to hp and graded versions of the time domain boundary element method for the weakly singular and the hypersingular integral equations. Numerical examples confirm the theoretical results for the Dirichlet and Neumann problems for screens and for polygonal domains in 2d. They exhibit the expected quasi-optimal convergence rates and the singular behavior of the solutions.

翻译：多面体域或屏幕外部区域中弹性动力学方程的解在角点和边缘处表现出奇异性。奇异性的详细展开意味着解的狄利克雷迹和牵引力的分段多项式逼近具有拟最优估计。这些结果被应用于弱奇异和超奇异积分方程的hp与分级时域边界元方法。数值算例验证了二维屏幕和多边形域上狄利克雷与诺伊曼问题的理论结果，展示了预期的拟最优收敛速率及解的奇异行为。