WIAS Preprint No. 1407, (2009)

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



Authors

  • Mielke, Alexander
    ORCID: 0000-0002-4583-3888
  • Paoli, Laetitia
  • Petrov, Adrien
  • Stefanelli, Ulisse

2010 Mathematics Subject Classification

  • 49J40, 74C05, 74N30

Keywords

  • shape-memory materials, evolutionary variational inequalities, rate-independent processes, space-time discretization, error estimates

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 the isothermal Souza-Auricchio model for shape-memory alloys.

Appeared in

  • SIAM J. Numer. Anal., 48 (2010) pp. 1625--1646.

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