A numerical verification for an unconditionally stable FEM for elastodynamics

Numerical results for a time-discontinuous Galerkin space-time finite element formulation for second-order hyperbolic partial differential equations are presented. Discontinuities are allowed at finite, but not fixed, time increments. A method for h-adaptive refinement of the space-time mesh is proposed and demonstrated. Numerical results are presented for linear elastic problems in one space dimension. Numerical verification of unconditional stability, as proven in [7], is rendered. Comparison is made with analytic solutions when available. It is shown that the accuracy of the numerical solution can be increased without a major penalty on computational cost by using an adaptively refined mesh. Results are presented for a type of solid-solid dynamic phase transition problem where the trajectory of a moving surface of discontinuity is tracked.