An adaptive finite element method for the inequality-constrained Reynolds equation

Tom Gustafsson, Kumbakonam R. Rajagopal, Rolf Stenberg*, Juha Videman

*Corresponding author for this work

Research output: Contribution to journalArticleScientificpeer-review

2 Citations (Scopus)


We present a stabilized finite element method for the numerical solution of cavitation in lubrication, modeled as an inequality-constrained Reynolds equation. The cavitation model is written as a variable coefficient saddle-point problem and approximated by a residual-based stabilized method. Based on our recent results on the classical obstacle problem, we present optimal a priori estimates and derive novel a posteriori error estimators. The method is implemented as a Nitsche-type finite element technique and shown in numerical computations to be superior to the usually applied penalty methods.

Original languageEnglish
Pages (from-to)156-170
Number of pages15
JournalComputer Methods in Applied Mechanics and Engineering
Publication statusPublished - 1 Jul 2018
MoE publication typeA1 Journal article-refereed


  • Reynolds equation
  • Stabilized finite element method
  • Variational inequality


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