A class of thermal sub-differential contact problems

We study a class of dynamic sub-differential contact problems with friction, and thermal effects, for time depending long memory visco-elastic materials, with or without the clamped condition. We describe the mechanical problem, derive its variational formulation, and after specifying the assumptions on the data and operators, we prove an existence and uniqueness of weak solution on displacement and temperature fields. Then we present a fully discrete scheme for numerical approximations of the different solutions, and provide analysis of error order estimates. Finally various numerical computations in dimension two will be given.