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On global spatial regularity and convergence rates for time-dependent elasto-plasticity. (English) Zbl 1207.35083

The author consider an elasto-plastic model in a geometrically linear framework for which the model class comprises rate independent elasto-plasticity with linear kinematic haedening combined with a von Mises flow rule or a Tresca flow rule, as well as elasto-visco-plastic models which include Cosserat effects. For this kind of models, considered on smooth domains, it is deduced the global spatial regularity of solutions, i.e., the regularity of displacements and of the internal variables. The basic result is based on a reflection argument which gives the regularity results in directions normal to the boundary on the basis of tangential regularity results. In the last part of the paper it is derived an estimate for the error between the theoretical solution and discrete solutions which are obtained from a finite element discretization in space and an implicit Euler scheme in time.
Reviewer: M. Marin (Brasov)

MSC:

35B65 Smoothness and regularity of solutions to PDEs
49N60 Regularity of solutions in optimal control
74C05 Small-strain, rate-independent theories of plasticity (including rigid-plastic and elasto-plastic materials)
74C10 Small-strain, rate-dependent theories of plasticity (including theories of viscoplasticity)
74S05 Finite element methods applied to problems in solid mechanics
65M55 Multigrid methods; domain decomposition for initial value and initial-boundary value problems involving PDEs
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