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 poly- gonal domains in 2d. They exhibit the expected quasi-optimal convergence rates and the singular behavior of the solutions.

多面体域或屏幕外部的弹性动力学方程的解从角和边表现出奇异行为。奇点的详细扩展意味着对解和牵引力的狄利克雷迹的分段多项式近似的准最优估计。结果应用于弱奇异和超奇异积分方程的时域边界元法的hp和分级版本。数值示例证实了 Dirichlet 和 Neumann 问题的理论结果，用于屏幕和 2d 中的多边形域。它们表现出预期的准最优收敛率和解的奇异行为。