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Zbl 0974.74055
Ben Belgacem, F.
Numerical simulation of some variational inequalities arisen from unilateral contact problems by the finite element methods. (English)
[J] SIAM J. Numer. Anal. 37, No.4, 1198-1216 (2000). ISSN 0036-1429; ISSN 1095-7170/e

This paper deals with the finite element approximation of variational inequalities coming from the Signorini problem on the unilateral contact between two elastic bodies. In the unilateral contact problem between two deformable solids, without friction, the authors consider a nonconforming finite element discretization. The discrete contact conditions are expressed, across the contact zone, using the mortar projection; former results are improved and optimal convergence rates are established under appropriate regularity hypotheses.\par The author concludes that variational inequalities as models of unilateral contact problems are of great interest in solid mechanics, and that, from the solid mechanics point of view, the regularity assumptions seem not to be stringent and are a fair modeling tool for realistic unilateral situations of engineering interest.
[Maria Agostina Vivaldi (Roma)]

MSC 2000:: *74S05 Finite element methods
74M15 Contact
49J40 Variational methods including variational inequalities

Keywords: unilateral contact problem; finite elements; variational inequalities; Signorini problem; unilateral contact; nonconforming finite element discretization; discrete contact conditions; mortar projection; optimal convergence rates; regularity

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