A sign preserving mixed finite element approximation for contact problems. (English) Zbl 1377.74023

Summary: This paper is concerned with the frictionless unilateral contact problem (i.e., a Signorini problem with the elasticity operator). We consider a mixed finite element method in which the unknowns are the displacement field and the contact pressure. The particularity of the method is that it furnishes a normal displacement field and a contact pressure satisfying the sign conditions of the continuous problem. The a priori error analysis of the method is closely linked with the study of a specific positivity preserving operator of averaging type which differs from the one of Z. Chen and R. H. Nochetto [Numer. Math. 84, No. 4, 527–548 (2000; Zbl 0943.65075)]. We show that this method is convergent and satisfies the same a priori error estimates as the standard approach in which the approximated contact pressure satisfies only a weak sign condition. Finally we perform some computations to illustrate and compare the sign preserving method with the standard approach.


74S05 Finite element methods applied to problems in solid mechanics
74M15 Contact in solid mechanics


Zbl 0943.65075
Full Text: DOI EuDML


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