Mathematics

In this talk a DG space-time FEM is presented that can correctly represent moving and stationary singular surfaces in boundary value problems of fully coupled thermo-elasto-dynamics. The proposed formulation is shown to be consistent and unconditionally stable. The key aspect of the formulation is that numerical stability is achieved by a physically-based approach consisting in enforcing the jump conditions of the balance of linear momentum and the balance of energy. The method's convergence rates are demonstrated using some exact solutions of two- and three-dimensional space-time boundary value problems. Solutions to boundary value problems with moving discontinuities are presented in which the degree of thermo-mechanical coupling is varied to show how the system's response in terms of stress, temperature, and energy release rate is affected.