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.
@article{bwmeta1.element.bwnjournal-article-amcv21i3p487bwm,
author = {Patrick Hild},
title = {A sign preserving mixed finite element approximation for contact problems},
journal = {International Journal of Applied Mathematics and Computer Science},
volume = {21},
year = {2011},
pages = {487-498},
zbl = {05999228},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-amcv21i3p487bwm}
}
Patrick Hild. A sign preserving mixed finite element approximation for contact problems. International Journal of Applied Mathematics and Computer Science, Tome 21 (2011) pp. 487-498. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-amcv21i3p487bwm/
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