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2002•Mathematics of ComputationOpen access

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

Ulisse Stefanelli

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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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What this paper is about

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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Available 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.

Key concepts: Discretization, Mathematics, Uniqueness, A priori and a posteriori, Convergence (economics), Applied mathematics, Discretization error, Variable (mathematics)

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