<abstract xml:lang="en" xmlns="http://www.w3.org/1999/xhtml"><p>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 <italic>a priori</italic> 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 Chen and Nochetto. We show that this method is convergent and satisfies the same <italic>a priori</italic> 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.</p></abstract>

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 Chen and Nochetto. 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.

A sign preserving mixed finite element approximation for contact problems

BesanécLon Laboratory of Mathematics, UMR CNRS 6623, Franche-ComtéeA University, 16 route de Gray, 25030 BesanécLon, France

International Journal of Applied Mathematics and Computer Science

{"article-title":"A sign preserving mixed finite element approximation for contact problems"}

This paper is concerned with the frictionless unilateral contact problem (i.e., a Signorini problem with the elasticity operator). We consider a mixed finite...

A sign preserving mixed finite element approximation for contact problems

Published Online: Sep 22, 2011

Page range: 487 - 498

DOI: https://doi.org/10.2478/v10006-011-0037-7

Keywords
variational inequality, positive operator, averaging operator, contact problem, Signorini problem, mixed finite element method

This content is open access.

A sign preserving mixed finite element approximation for contact problems

Published Online: Sep 22, 2011

Page range: 487 - 498

DOI: https://doi.org/10.2478/v10006-011-0037-7

Keywordsvariational inequality, positive operator, averaging operator, contact problem, Signorini problem, mixed finite element method

This content is open access.

Keywords
variational inequality, positive operator, averaging operator, contact problem, Signorini problem, mixed finite element method