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Numerical analysis of a relaxed variational model of hysteresis in two-phase solids. (English) Zbl 1007.74062

This paper presents the numerical analysis of a variational formulation of rate-independent phase transformations in elastic solids. The model itself suggests an implicit time discretization which is combined with finite element method in space. A priori error estimates are established for the quasioptimal spatial approximation of stress field within one time step. A posteriori error estimates motivate an adaptive mesh-refining algorithm for efficient discretization.

MSC:

74N30 Problems involving hysteresis in solids
74S05 Finite element methods applied to problems in solid mechanics
65N15 Error bounds for boundary value problems involving PDEs
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