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 nary 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. ication of the abstract theory to a semilinear case is detailed. In particular, we provide explicit space-time convergence rates for the isothermal Souza-Auricchio model for shape-memory alloys. Key words. Shape-memory materials, evolutionary variational inequalities, rate-independent processes, space-time discretization, error estimates. AMS subject classifications. 49J40, 74C05, 74N30

• Type: Journal
• Year: 2010
• Where: SIAMNUM
• Authors: Alexander Mielke, Laetitia Paoli, Adrien Petrov, Ulisse Stefanelli
• Keywords: Error Estimates, SIAMNUM 2010, Space-time Discretization, Variational Inequalities