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
Publication type: Journal Article
Publication date: 2017-11-02
Journal:
SIAM Journal on Numerical Analysis
Q1
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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Burman E., Hansbo P., Larson M. G. The Penalty-Free Nitsche Method and Nonconforming Finite Elements for the Signorini Problem // SIAM Journal on Numerical Analysis. 2017. Vol. 55. No. 6. pp. 2523-2539.
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Burman E., Hansbo P., Larson M. G. The Penalty-Free Nitsche Method and Nonconforming Finite Elements for the Signorini Problem // SIAM Journal on Numerical Analysis. 2017. Vol. 55. No. 6. pp. 2523-2539.
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RIS
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TY - JOUR
DO - 10.1137/16m107846x
UR - https://doi.org/10.1137/16m107846x
TI - The Penalty-Free Nitsche Method and Nonconforming Finite Elements for the Signorini Problem
T2 - SIAM Journal on Numerical Analysis
AU - Burman, Erik
AU - Hansbo, Peter
AU - Larson, Mats G.
PY - 2017
DA - 2017/11/02
PB - Society for Industrial and Applied Mathematics (SIAM)
SP - 2523-2539
IS - 6
VL - 55
SN - 0036-1429
SN - 1095-7170
ER -
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BibTex (up to 50 authors)
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@article{2017_Burman,
author = {Erik Burman and Peter Hansbo and Mats G. Larson},
title = {The Penalty-Free Nitsche Method and Nonconforming Finite Elements for the Signorini Problem},
journal = {SIAM Journal on Numerical Analysis},
year = {2017},
volume = {55},
publisher = {Society for Industrial and Applied Mathematics (SIAM)},
month = {nov},
url = {https://doi.org/10.1137/16m107846x},
number = {6},
pages = {2523--2539},
doi = {10.1137/16m107846x}
}
Cite this
MLA
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Burman, Erik, et al. “The Penalty-Free Nitsche Method and Nonconforming Finite Elements for the Signorini Problem.” SIAM Journal on Numerical Analysis, vol. 55, no. 6, Nov. 2017, pp. 2523-2539. https://doi.org/10.1137/16m107846x.