On Nitsche's method for elastic contact problems

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We show quasi-optimality and a posteriori error estimates for the frictionless contact problem between two elastic bodies with a zero-gap function. The analysis is based on interpreting Nitsche's method as a stabilized finite element method for which the error estimates can be obtained with minimal regularity assumptions and without the saturation assumption. We present three different Nitsche's mortaring techniques for the contact boundary, each corresponding to a different stabilizing term. Our numerical experiments show the robustness of Nitsche's method and corroborate the efficiency of the a posteriori error estimators.

Original languageEnglish
Pages (from-to)B425-B446
Number of pages22
JournalSIAM Journal on Scientific Computing
Issue number2
Publication statusPublished - 2020
MoE publication typeA1 Journal article-refereed


  • Elastic contact
  • Nitsche's method
  • Variational inequality


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