Space-time finite element methods for second-order hyperbolic equations (Q1179086)

A modification of finite element method to solve elastodynamics problems is presented. The authors use finite elments to discretize the temporal domain as well as the spatial domain. Linear stabilizing mechanisms are included and nonlinear discontinuity-capturing operators are used to improve the performance of the algorithm in regions where the solution exhibits large gradients. Stability and convergence of the method are proved. The method is illustrated by solving two test problems: the first is the problem of the impact against the rigid wall of a one-dimensional homogeneous elastic bar, the another is the wave propagation problem for a bar consisting of two different materials.