Solution of linear elastodynamics problems with space–time finite elements on structured and unstructured meshes

A new implicit approach for the solution of linear elastodynamics problems on structured and unstructured meshes with space–time finite elements is suggested. New weak formulations are based on time continuous (TCG) and discontinuous (TDG) Galerkin methods. It was shown that for structured meshes, the new TCG method has a higher order of accuracy (by a factor of two) than that of the standard TCG method. At the same number of degrees of freedom the accuracy of the new TCG method is one order higher than the accuracy of the standard TDG method. The introduction of new weighting functions for the weak formulations of the TCG and TDG methods allows control of the high frequency behavior without degradation of accuracy of the methods. A variable number of elements in the time direction as well as a variable order of polynomial time approximations of finite elements for time slabs allows the implementation of a coupled space–time adaptive procedure using structured or unstructured meshes. Numerical examples for 1-D problems demonstrate the effectiveness of the technique.