A priori error estimation for elasto-hydrodynamic lubrication using interior-exterior penalty approach

TL;DR

This paper develops an interior-exterior penalty discontinuous Galerkin finite element method for elastohydrodynamic lubrication problems, providing theoretical error estimates and validating them through numerical experiments.

Contribution

It introduces a novel DG-FEM approach with a priori error estimates for EHL problems, including existence and uniqueness proofs.

Findings

Optimal error estimates in $L^{2}$ and $H^{1}$ norms

Method's validity confirmed by numerical experiments

Solution existence and uniqueness established

Abstract

In the present study, an interior-exterior penalty discontinuous Galerkin finite element method (DG-FEM) is analysed for solving Elastohydrodynamic lubrication (EHL) line and point contact problems. The existence of discrete penalized solution is examined using Brouwer's fixed point theorem. Furthermore, the uniqueness of solution is proved using Lipschitz continuity of the discrete solution map under light load parameter assumptions. A priori error estimates are achieved in $L^{2}$ and $H^{1}$ norms which are shown to be optimal in mesh size $h$ and suboptimal in polynomial degree $p$. The validity of theoretical findings are confirmed through series of numerical experiments.