Nitsche's method for unilateral contact problems

Research output: Contribution to journalArticleScientificpeer-review


Research units

  • VTT Technical Research Centre of Finland
  • University of Lisbon


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.


Original languageEnglish
Pages (from-to)189-204
Number of pages16
Issue number3-4
Publication statusPublished - 1 Jan 2018
MoE publication typeA1 Journal article-refereed

    Research areas

  • A posteriori estimate, Nitsche's method, Stabilised finite elements, Unilateral contact

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