Proof of unconditional stability for a single-field discontinuous Galerkin finite element formulation for linear elasto-dynamics

A discontinuous Galerkin (DG) finite element method (FEM) for the solution of linear elasto-dynamic problems is revisited and modified. The new DG FEM is based on a method originally proposed by [Comput. Methods Appl. Mech. Engrg. 84 (1990) 327] and recently adapted by [Comput. Methods Appl. Mech. Engrg. 191(46) (2002) 5315] for the solution of dynamic solid–solid phase transitions. As the FEM formulations in both the cited works have been found not to be unconditionally stable in cases where the underlying FEM grid is completely unstructured, this paper offers a modification of these formulations yielding a single-field DG FEM that is unconditionally stable without any restrictions on the grid structure. Furthermore, an energy conserving variant of the formulation is also suggested.