Stable finite element methods for the Reynolds equation in elastohydrodynamic lubrication problems

Abstract

This thesis focuses on the development of stable finite element methods for the Reynolds equation in elastohydrodynamic lubrication (EHL) problems. Building upon existing stabilized methods for convection-diffusion problems, a hybrid discontinuous Galerkin (HDG) and a hybrid mixed three-field (HM3F) formulation are introduced and compared with the streamline upwind Petrov-Galerkin (SUPG) method. Furthermore, a mass-conserving cavitation model based on the Jakobsson-Floberg-Olsson (JFO) conditions is presented. The coupling of the Reynolds equation with elasticity, film thickness and load balance equations to obtain the EHL system is discussed for circular contact problems and problems with arbitrary geometries. The computational performance and the stability of the different finite element methods is assessed through numerical experiments.