Analysis of a Contact Problem Problem Involving an Elastic Body with Dual-Phase-Lag

In this work we study a contact problem between a thermoelastic body with dual-phase-lag and a deformable obstacle. The contact is modelled using a modification of the well-known normal compliance contact condition. An existence and uniqueness result is proved applying the Faedo–Galerkin method and Gronwall’s inequality. The exponential stability is also shown. Then, we introduce a fully discrete approximation by using the implicit Euler scheme and the finite element method. A discrete stability property and a priori error estimates are obtained, from which the linear convergence of the algorithm is derived under suitable regularity conditions. Finally, some numerical examples are presented to demonstrate the accuracy of the approximation and the behaviour of the solution.