Numerical analysis of a relaxed variational model of hysteresis in two-phase solids
Carsten Carstensen and Petr Plechac
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Submission date: 10. Dec. 2000
published in: RAIRO / Mathematical modelling and numerical analysis, 35 (2001) 5, p. 865-878
MSC-Numbers: 65N30, 73C05
Keywords and phrases: variational problem, phase transitions, elasticity, hysteresis, a-priori error estimates, a-posteriori estimates, adaptive algorithms, non-convex minimization, microstructure
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This paper presents the numerical analysis for a variational formulation of rate-independent phase transformations in elastic solids due to Mielke et al. The new model itself suggests an implicit time-discretization which is combined with the finite element method in space. A priori error estimates are established for the quasioptimal spatial approximation of the stress field within one time-step. A posteriori error estimates motivate an adaptive mesh-refining algorithm for efficient discretization. The proposed scheme enables numerical simulations which show that the model allows for hysteresis.