An adaptive finite element method for the inequality-constrained Reynolds equation
Provides a more accurate numerical method for simulating cavitation in lubrication, which is important for engineering applications involving bearings and seals.
The paper presents a stabilized finite element method for solving the inequality-constrained Reynolds equation modeling cavitation in lubrication, demonstrating superiority over penalty methods in numerical computations.
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.