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

Authors:
Alexander Mielke;Laetitia Paoli;Adrien Petrov;Ulisse Stefanelli
Affiliations:
mielke@wias-berlin.de;laetitia.paoli@univ-st-etienne.fr;petrov@wias-berlin.de;ulisse.stefanelli@imati.cnr.it
Venue:
SIAM Journal on Numerical Analysis
Year:
2010

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Abstract

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.