A space-time discontinuous Galerkin method for linearized elastodynamics with element-wise momentum balance

We present a new space-time discontinuous Galerkin finite element method for linearized elastodynamics that delivers exact balance of linear and angular momentum over every space-time element. The method is formulated for use with fully unstructured space-time grids and uses displacement basis functions that are discontinuous across all inter-element boundaries. We introduce a new space-time formulation of continuum elastodynamics that uses differential forms and the exterior calculus on manifolds to generate a system of space-time field equations and jump conditions. Then we invoke a Bubnov-Galerkin weighted residuals procedure to formulate the finite element method. We describe an implementation on patch-wise causal meshes that features linear complexity in the number of elements and special per-pixel accurate visualization. Numerical examples confirm an a priori error estimate and demonstrate the method's shock-capturing capabilities.