A new hybrid velocity integration method applied to elastic wave propagation

We present a novel space–time Galerkin method for solutions of second-order time-dependent problems. By introducing the displacement–velocity relationship implicitly, the governing set of equations is reformulated into a first-order single field problem with the unknowns in the velocity field. The resulting equation is in turn solved by a time-discontinuous Galerkin approach (Int. J. Numer. Anal. Meth. Geomech. 2006; 30:1113–1134), in which the continuity between time intervals is weakly enforced by a special upwind flux treatment. After solving the equation for the unknown velocities, the displacement field quantities are computed a posteriori in a post-processing step. Various numerical examples demonstrate the efficiency and reliability of the proposed method. Convergence studies with respect to the h- and p-refinement and different discretization techniques are given.