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Analysis of a variable time-step discretization of the three-dimensional Frémond model for shape memory alloys


Author: Ulisse Stefanelli
Journal: Math. Comp. 71 (2002), 1431-1453
MSC (2000): Primary 80A22, 35K55, 65M15
DOI: https://doi.org/10.1090/S0025-5718-02-01409-6
Published electronically: January 17, 2002
MathSciNet review: 1933039
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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.


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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

DOI: https://doi.org/10.1090/S0025-5718-02-01409-6
Keywords: Shape memory alloys, time discretization, existence and uniqueness, error estimate
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
Article copyright: © Copyright 2002 American Mathematical Society

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