Thermo-mechanical contact problems on non-matching meshes

Non-matching meshes and domain decomposition techniques based on Lagrange multipliers provide a flexible and efficient discretization technique for variational inequalities with interface constraints. Although mortar methods are well analyzed for variational inequalities, its application to dynamic thermo-mechanical contact problems with friction is still a field of active research. In this work, we extend the mortar approach for dynamic contact problems with Coulomb friction to the thermo-mechanical case. We focus on the discretization and on algorithmic aspects of dynamic effects such as frictional heating and thermal softening at the contact interface. More precisely, we generalize the mortar concept of dual Lagrange multipliers to non-linear Robin-type interface conditions and apply local static condensation to eliminate the heat flux. Numerical examples in the two-dimensional and the three-dimensional setting illustrate the flexibility of the discretization on non-matching meshes.