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Portugaliae Mathematica

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Volume 75, Issue 3/4, 2018, pp. 189–204
DOI: 10.4171/PM/2016

Published online: 2019-06-06

Nitsche’s method for unilateral contact problems

Tom Gustafsson[1], Rolf Stenberg[2] and Juha H. Videman[3]

(1) VTT Technical Research Centre of Finland Ltd., Espoo, Finland
(2) Aalto University, Finland
(3) Instituto Superior Técnico, Lisboa, Portugal

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.

Keywords: Nitsche’s method, unilateral contact, stabilised finite elements, a posteriori estimate

Gustafsson Tom, Stenberg Rolf, Videman Juha: Nitsche’s method for unilateral contact problems. Port. Math. 75 (2018), 189-204. doi: 10.4171/PM/2016