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On the solution of a finite element approximation of a linear obstacle plate problem

100%
Fernandes L. M., Figueiredo I. N., Júdice J. J.
International Journal of Applied Mathematics and Computer Science
|
2002
|
tom 12
|
nr 1
27-40
EN
In this paper the solution of a finite element approximation of a linear obstacle plate problem is investigated. A simple version of an interior point method and a block pivoting algorithm have been proposed for the solution of this problem. Special purpose implementations of these procedures are included and have been used in the solution of a set of test problems. The results of these experiences indicate that these procedures are quite efficient to deal with these instances and compare favourably with the path-following PATH and the active-set MINOS codes of the commercial GAMS collection.
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A sign preserving mixed finite element approximation for contact problems

75%
Hild P.
International Journal of Applied Mathematics and Computer Science
|
2011
|
tom 21
|
nr 3
487-498
EN
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.
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