We derive optimal a priori and a posteriori error estimates for Nitsche’s method applied to unilateral contact problems. Our analysis is based on the interpretation of Nitsche’s method as a stabilised finite element method for the mixed Lagrange multiplier formulation of the contact problem wherein the Lagrange multiplier has been eliminated elementwise. To simplify the presentation, we focus on the scalar Signorini problem and outline only the proofs of the main results since most of the auxiliary results can be traced to our previous works on the numerical approximation of variational inequalities. We end the paper by presenting results of our numerical computations which corroborate the efficiency and reliability of the a posteriori estimators.
%0 Journal Article
%1 gustafsson2019nitsches
%A Gustafsson, Tom
%A Stenberg, Rolf
%A Videman, Juha
%D 2019
%I European Mathematical Society Publishing House
%J Portugaliae Mathematica
%K 65n30-pdes-bvps-finite-elements 74b05-classical-linear-elasticity 74m15-contact-mechanics-of-deformable-solids 74s05-finite-element-methods-for-solid-mechanics
%N 3
%P 189--204
%R 10.4171/pm/2016
%T Nitsche's method for unilateral contact problems
%U https://www.ems-ph.org/journals/show_abstract.php?issn=0032-5155&vol=75&iss=3&rank=2
%V 75
%X We derive optimal a priori and a posteriori error estimates for Nitsche’s method applied to unilateral contact problems. Our analysis is based on the interpretation of Nitsche’s method as a stabilised finite element method for the mixed Lagrange multiplier formulation of the contact problem wherein the Lagrange multiplier has been eliminated elementwise. To simplify the presentation, we focus on the scalar Signorini problem and outline only the proofs of the main results since most of the auxiliary results can be traced to our previous works on the numerical approximation of variational inequalities. We end the paper by presenting results of our numerical computations which corroborate the efficiency and reliability of the a posteriori estimators.
@article{gustafsson2019nitsches,
abstract = {
We derive optimal a priori and a posteriori error estimates for Nitsche’s method applied to unilateral contact problems. Our analysis is based on the interpretation of Nitsche’s method as a stabilised finite element method for the mixed Lagrange multiplier formulation of the contact problem wherein the Lagrange multiplier has been eliminated elementwise. To simplify the presentation, we focus on the scalar Signorini problem and outline only the proofs of the main results since most of the auxiliary results can be traced to our previous works on the numerical approximation of variational inequalities. We end the paper by presenting results of our numerical computations which corroborate the efficiency and reliability of the a posteriori estimators. },
added-at = {2020-06-04T06:09:03.000+0200},
author = {Gustafsson, Tom and Stenberg, Rolf and Videman, Juha},
biburl = {https://www.bibsonomy.org/bibtex/2ac30d4fe556678a5a4b414268febd59c/gdmcbain},
doi = {10.4171/pm/2016},
interhash = {c8843452a89af0b62545530ae16c1d92},
intrahash = {ac30d4fe556678a5a4b414268febd59c},
issn = {0032-5155},
journal = {Portugaliae Mathematica},
keywords = {65n30-pdes-bvps-finite-elements 74b05-classical-linear-elasticity 74m15-contact-mechanics-of-deformable-solids 74s05-finite-element-methods-for-solid-mechanics},
month = jun,
number = 3,
pages = {189--204},
publisher = {European Mathematical Society Publishing House},
timestamp = {2020-06-04T06:09:03.000+0200},
title = {Nitsche's method for unilateral contact problems},
url = {https://www.ems-ph.org/journals/show_abstract.php?issn=0032-5155&vol=75&iss=3&rank=2},
volume = 75,
year = 2019
}