SIAM Journal on Numerical Analysis, volume 55, issue 6, pages 2523-2539
The Penalty-Free Nitsche Method and Nonconforming Finite Elements for the Signorini Problem
Erik Burman
,
Peter Hansbo
,
Mats G. Larson
Publication type: Journal Article
Publication date: 2017-11-02
Journal:
SIAM Journal on Numerical Analysis
scimago Q1
SJR: 2.163
CiteScore: 4.8
Impact factor: 2.8
ISSN: 00361429, 10957170
Computational Mathematics
Applied Mathematics
Numerical Analysis
Abstract
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.
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