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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.

MSC:

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

Citations:

Zbl 0943.65075
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References:

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