An adaptive finite element method for the inequality-constrained Reynolds equation
Numerical Analysis
2018-05-09 v2
Abstract
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.
Cite
@article{arxiv.1711.04274,
title = {An adaptive finite element method for the inequality-constrained Reynolds equation},
author = {Tom Gustafsson and K. R. Rajagopal and Rolf Stenberg and Juha Videman},
journal= {arXiv preprint arXiv:1711.04274},
year = {2018}
}