An h–adaptive Spacetime–Discontinuous Galerkin Method for Linearized Elastodynamics

We present an h–adaptive version of the spacetime–discontinuous Galerkin (SDG) finite element method for linearized elastodynamics (Abedi et al., 2005) that is particularly well suited to multiscale simulations and to problems involving shocks. The adaptive version inherits key properties of the basic SDG formulation, including element-wise balance of linear and angular momentum, complexity that is linear in the number of elements and oscillation– free shock capturing. Unstructured spacetime grids allow simultaneous adaptation in space and time, and support for nonconforming meshes simplifies refinement and coarsening in response to a dissipation–based error indicator. A localized patch–by–patch solution process limits the cost of reanalysis when the error indicator calls for more refinement. Numerical examples demonstrate the method’s performance and shock–capturing capabilities. RÉSUMÉ.