Error estimates for space-time discretizations of a rate-independent variational inequality
- Mielke, Alexander
- Paoli, Laetitia
- Petrov, Adrien
- Stefanelli, Ulisse
2010 Mathematics Subject Classification
- 49J40, 74C05, 74N30
- shape-memory materials, evolutionary variational inequalities, rate-independent processes, space-time discretization, error estimates
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 the isothermal Souza-Auricchio model for shape-memory alloys.
- SIAM J. Numer. Anal., 48 (2010) pp. 1625--1646.