Analysis and numerical approximation of a dynamic contact problem with friction and adhesion
Volume 45 / 2018
Applicationes Mathematicae 45 (2018), 103-127
MSC: 47J20, 65M60, 74M10, 74M15.
DOI: 10.4064/am2323-6-2017
Published online: 15 January 2018
Abstract
We study a dynamic contact problem for viscoelastic materials with long-term memory. The contact is modelled with a coupled system of Tresca’s friction law and an ordinary differential equation which describes the adhesion effect. Under appropriate assumptions, we provide a weak formulation of the mechanical problem and establish the existence and uniqueness of a weak solution. We then introduce a fully discrete scheme for the model. We derive error estimates, and under suitable regularity assumptions we derive a linear convergence result.
