# A sign preserving mixed finite element approximation for contact problems

• Volume: 21, Issue: 3, page 487-498
• ISSN: 1641-876X

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## Abstract

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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.

## How to cite

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Patrick Hild. "A sign preserving mixed finite element approximation for contact problems." International Journal of Applied Mathematics and Computer Science 21.3 (2011): 487-498. <http://eudml.org/doc/208063>.

@article{PatrickHild2011,
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.},
author = {Patrick Hild},
journal = {International Journal of Applied Mathematics and Computer Science},
keywords = {variational inequality; positive operator; averaging operator; contact problem; Signorini problem; mixed finite element method},
language = {eng},
number = {3},
pages = {487-498},
title = {A sign preserving mixed finite element approximation for contact problems},
url = {http://eudml.org/doc/208063},
volume = {21},
year = {2011},
}

TY - JOUR
AU - Patrick Hild
TI - A sign preserving mixed finite element approximation for contact problems
JO - International Journal of Applied Mathematics and Computer Science
PY - 2011
VL - 21
IS - 3
SP - 487
EP - 498
AB - 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.
LA - eng
KW - variational inequality; positive operator; averaging operator; contact problem; Signorini problem; mixed finite element method
UR - http://eudml.org/doc/208063
ER -

## References

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