Mortar finite elements for a heat transfer problem on sliding meshes

We consider a heat transfer problem with sliding bodies, where heat is generated on the interface due to friction. Neglecting the mechanical part, we assume that the pressure on the contact interface is a known function. Using mortar techniques with Lagrange multipliers, we show existence and uniqueness of the solution in the continuous setting. Moreover, two different mortar formulations are analyzed, and optimal a priori estimates are provided. Numerical results illustrate the flexibility of the approach.