Time discontinuous Galerkin methods with energy decaying correction fornon-linear elastodynamics

In this paper a new time discontinuous Galerkin TDG formulation for nonlinear elastodynamics is presented. The new formulation embeds an energy correction which ensures truly energy decaying, thus allowing to achieve unconditional stability that, as shown in the paper, is not guaranteed by the classical TDG formulation. The resulting method is simple and easily implementable into existing finite element codes. Moreover, it inherits the desirable higherorder accuracy and highfrequency dissipation properties of the classical formulation. Numerical results illustrate the very good performance of the proposed formulation. Copyright \ua9 2010 John Wiley & Sons, Ltd