Time discontinuous Galerkin methods with energy decaying correction for non-linear elastodynamics

In this paper a new time discontinuous Galerkin formulation for non-linear elastodynamics is presented. The new formulation embeds an energy correction which ensures truly energy decaying so allowing to achieve unconditional stability that, as shown in the paper, is not guaranteed by the classical time discontinuous Galerkin formulation. The resulting method is simple and easily implementable into existing finite element codes. Moreover, it inherits the desirable higher-order accuracy and high-frequency dissipation properties of the classical formulation. Numerical results illustrate the very good performance of the proposed formulation.