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Error Bounds for Space-Time Discretizations of a 3D Model for Shape-Memory Materials

  • Alexander Mielke
  • Laetitia Paoli
  • Adrien Petrov
  • Ulisse Stefanelli
Conference paper
Part of the IUTAM Bookseries book series (IUTAMBOOK, volume 21)

Abstract

This paper deals with error estimates for space-time discretizations of a three-dimensional model for isothermal stress-induced transformations in shapememory materials. After recalling existence and uniqueness results, a fully-discrete approximation is presented and an explicit space-time convergence rate of order \(h^{\alpha/2} + \tau^{1/2}\) for some α ∈ (0,1] is derived.

Keywords

Galerkin Projector Solid Phase Transformation Induce Phase Transformation Quasistatic Evolution M2AN Math 
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Copyright information

© Springer Science+Business Media B.V. 2010

Authors and Affiliations

  • Alexander Mielke
    • 1
  • Laetitia Paoli
    • 2
  • Adrien Petrov
    • 1
  • Ulisse Stefanelli
    • 3
  1. 1.Weierstraß-Institut für Angewandte Analysis und StochastikBerlinGermany
  2. 2.LaMUSE (Laboratoire de Mathématiques de l’Université de Saint-Etienne)Saint-Etienne Cedex 02France
  3. 3.Istituto di Matematica Applicata e Tecnologie Informatiche – CNRPaviaItaly

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