Error Estimates for Space-Time Discretizations of a Rate-Independent Variational Inequality

@article{Mielke2010ErrorEF,
  title={Error Estimates for Space-Time Discretizations of a Rate-Independent Variational Inequality},
  author={Alexander Mielke and Laetitia Paoli and Adrien Petrov and Ulisse Stefanelli},
  journal={SIAM J. Numer. Anal.},
  year={2010},
  volume={48},
  pages={1625-1646}
}
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… 
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