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The Penalty-Free Nitsche Method and Nonconforming Finite Elements for the Signorini Problem
Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics.
2017 (English)In: SIAM Journal on Numerical Analysis, ISSN 0036-1429, E-ISSN 1095-7170, Vol. 55, no 6, p. 2523-2539Article in journal (Refereed) Published
Abstract [en]

We design and analyse a Nitsche method for contact problems. Compared to the seminal work of Chouly and Hild [SIAM J. Numer. Anal., 51 ( 2013), pp. 1295-1307], our method is constructed by expressing the contact conditions in a nonlinear function for the displacement variable instead of the lateral forces. The contact condition is then imposed using the nonsymmetric variant of Nitsche's method that does not require a penalty term for stability. Nonconforming piecewise affine elements are considered for the bulk discretization. We prove optimal error estimates in the energy norm.

Place, publisher, year, edition, pages
Society for Industrial and Applied Mathematics, 2017. Vol. 55, no 6, p. 2523-2539
Keywords [en]
finite element, Nitsche's method, contact, Signorini problem
National Category
Computational Mathematics
Identifiers
URN: urn:nbn:se:umu:diva-143957DOI: 10.1137/16M107846XISI: 000418663500001OAI: oai:DiVA.org:umu-143957DiVA, id: diva2:1174014
Available from: 2018-01-15 Created: 2018-01-15 Last updated: 2018-06-09Bibliographically approved

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Larson, Mats G.

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