# A sign preserving mixed finite element approximation for contact problems

International Journal of Applied Mathematics and Computer Science (2011)

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

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topPatrick 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 -

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