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

作者：Gustafsson Tom; Rajagopal Kumbakonam R; Stenberg Rolf^*; Videman Juha

来源：Computer Methods in Applied Mechanics and Engineering, 2018, 336: 156-170.

DOI：10.1016/j.cma.2018.03.004

• Reynolds equation
• Variational inequality
• Stabilized finite element method

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.

• 出版日期2018-7-1