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arXiv · 1711.04274

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

Tom Gustafsson·K. R. Rajagopal·Rolf Stenberg·Juha Videman
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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.

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Tom Gustafsson, K. R. Rajagopal, Rolf Stenberg, Juha Videman. 2017-11-12. An adaptive finite element method for the inequality-constrained Reynolds equation. https://doi.org/10.1016/j.cma.2018.03.004

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