Implementation and adaptivity of a space-time finite element method for structural dynamics Original Research Article

In this paper we study the implementation and adaptivity of a space-time finite element method for the analysis of two-dimensional problems in structural dynamics. The method, also known as the time-discontinuous Galerkin method or the DG method, employs finite elements discretizations in space and time simultaneously with bilinear basis functions that are continuous in space and discontinuous in time. Based on using the Zienkiewicz-Zhu error estimate in space and the jumps (discontinuities) of displacements and velocities in the total energy norm as a local error estimate in time, an h-adaptive procedure which updates the spatial mesh and the time step size automatically so as to control the estimated errors within specified tolerances is proposed. Numerical examples are presented, showing that the considered DG method is of second-order accuracy in space (in L2) and third-order accuracy in time, and the adaptive procedure is capable of updating the spatial meshes and the time steps when necessary, making the solutions reliable and the computation efficient.