Analysis of a variable time-step discretization of the three-dimensional Frémond model for shape memory alloys
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Abstract:
This paper deals with a semi-implicit time discretization with variable step of a three-dimensional Frémond model for shape memory alloys. Global existence and uniqueness of a solution is discussed. Moreover, an a priori estimate for the discretization error is recovered. The latter depends solely on data, imposes no constraints between consecutive time steps, and shows an optimal order of convergence when referred to a simplified model.References
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Additional Information
- Ulisse Stefanelli
- Affiliation: Dipartimento di Matematica, Università di Pavia, via Ferrata 1, 27100 Pavia, Italy
- Email: ulisse@dimat.unipv.it
- Received by editor(s): September 8, 1999
- Received by editor(s) in revised form: October 23, 2000
- Published electronically: January 17, 2002
- Additional Notes: This work has been partially supported by the Istituto di Analisi Numerica del CNR, Pavia, Italy
- © Copyright 2002 American Mathematical Society
- Journal: Math. Comp. 71 (2002), 1431-1453
- MSC (2000): Primary 80A22, 35K55, 65M15
- DOI: https://doi.org/10.1090/S0025-5718-02-01409-6
- MathSciNet review: 1933039