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Finite element approximation of an evolution problem modeling shear band formation. (English) Zbl 0848.73064
Summary: An error analysis is provided for the spatial approximation by the finite element method of a nonlinear time-dependent problem which models the antiplane shear deformations of a thermoplastic material. This problem consists of a system of two coupled partial differential equations with velocity and temperature as unknowns. Optimal order error estimates in the \(L^2\)-norm are given for each of these.

MSC:
74S05 Finite element methods applied to problems in solid mechanics
74C99 Plastic materials, materials of stress-rate and internal-variable type
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