Error estimates for space-time discretizations of a rate-independent variational inequality

This paper deals with error estimates for space-time discretizations in the context of evolutionary variational inequalities of rate-independent type. After introducing a general abstract evolution problem, we address a fully discrete approximation and provide a priori error estimates. The application of the abstract theory to a semilinear case is detailed. In particular, we provide explicit space-time convergence rates for classical strain gradient plasticity and the isothermal Souza-Auricchio model for shape-memory alloys