Analysis of a parabolic bilateral obstacle problem with non-monotone relations in the domain

Abstract

In this paper, we consider a new parabolic bilateral obstacle model. Both upper and lower obstacles are elastic-rigid and assign a non-monotone reactive normal pressure with respect to the interpenetration. The weak form of the model is a parabolic variational–hemivariational inequality with non-monotone multivalued relations in the domain. We show the existence and uniqueness of the solution. Then, a fully discrete numerical method is introduced, with the approximations can be internal or external. We bound the error estimates and obtain the Céa type inequality. Using the linear finite elements, the optimal-order error estimates are derived. Finally, we report the numerical simulation results.