Finite element approximations to an evolutionary variational inequality with a volterra term

In the first part of this paper, we briefly describe a mathematical model for the simulation of the injection moulding process of a plastic melt into a mould cavity. Using Baiocchi transformation, the problem is transformed into an evolutionary variational inequality with a Volterra term. Based on penalty method, existence, uniqueness and regularity results are discussed. Finally, a finite element Galerkin procedure is applied and a priori error estimates are derived.