Numerical analysis of a viscoelastic contact problem

We consider a mathematical model which describes the frictional contact between a viscoelastic body and an obstacle, the so-called foundation. The process is quasistatic and the behavior of the material is modeled with a constitutive law with long memory. The contact is bilateral and the friction is modeled with Tresca’s law. The existence of a unique weak solution to the model was proved in [15]. Here we describe a fully discrete scheme for the problem, implement it in a computer code and provide numerical results in the study of a two-dimensional test problem. 2000 Mathematics Subject Classification. Primary 74M15; Secondary 65M60.