Belhachmi, Zakaria; Tahir, Souad Mixed finite element discretization of some variational inequalities arising in elasticity problems in domains with cracks. (English) Zbl 1077.74045 Electron. J. Differ. Equ. 2004, Conf. 11, 33-40 (2004). 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. MSC: 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 Keywords:augmented Lagrangian formulation; convergence rates; optimal error estimates PDFBibTeX XMLCite \textit{Z. Belhachmi} and \textit{S. Tahir}, Electron. J. Differ. Equ. 2004, 33--40 (2004; Zbl 1077.74045) Full Text: EuDML EMIS