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

Research output: Contribution to journalArticleScientificpeer-review


Research units

  • Texas A and M University
  • Instituto Superior Tecnico Lisboa


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

    Research areas

  • Reynolds equation, Stabilized finite element method, Variational inequality

ID: 18844212