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Mixed finite element discretization of some variational inequalities arising in elasticity problems in domains with cracks. (English) Zbl 1077.74045
Summary: We consider some mixed variational formulations of elasticity system in domains with cracks. Inequality-type conditions are prescribed at the crack faces, which results in a model of unilateral contact. Relying on a new variational formulation of these problems in the smooth domain, we study and implement various mixed finite element methods. We derive convergence rates and optimal error estimates.
74S05 Finite element methods applied to problems in solid mechanics
74M15 Contact in solid mechanics
74B05 Classical linear elasticity
74R10 Brittle fracture
49J40 Variational inequalities
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