A sign preserving mixed finite element approximation for contact problems

• Autorzy: Hild P.
• Języki publikacji: EN

Abstrakty

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.

Słowa kluczowe

EN

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

PL

nierówność wariacyjna; zagadnienie kontaktowe; metoda elementów skończonych

• Wydawca: Oficyna Wydawnicza Uniwersytetu Zielonogórskiego
• Czasopismo: International Journal of Applied Mathematics and Computer Science
• Rocznik: 2011
• Tom: Vol. 21, no 3
• Strony: 487--498
• Opis fizyczny: Bibliogr. 33 poz., tab., wykr.

Twórcy

autor

Hild P.

• Besançon Laboratory of Mathematics, UMR CNRS 6623 Franche-Comté University, 16 route de Gray, 25030 Besançon, France,

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