Convergence and error estimates for finite element solutions of elastohydrodynamic lubrication
type: Item
instance of: scholarly article
title: Convergence and error estimates for finite element solutions of elastohydrodynamic lubrication
zbMATH Open document ID: 0617.76004
DOI: 10.1016/0898-1221(87)90119-2
author: Yanyan Li
publication date: 1987-01-01T00:00:00Z
review text: By using a formulation of elastohydrodynamic lubrication (EHL) problems which employs a nonlinear variational inequality and an exterior penalty method, convergence of finite element approximations to the EHL problem is studied. It is shown that the finite element method for the penalized problem is convergent. Then an a priori error estimate of the finite element solution is derived. Numerical experiments are performed for both line contact and point contact problems. In cases of light loads, first- order convergence in the \(H^ 1\)-norm for pressure approximation by linear elements and second-order convergence for quadratic elements are achieved as predicted. One order higher convergence in the \(L^ 2\)-norm is also observed as expected.
Mathematics Subject Classification ID: 76A05
Mathematics Subject Classification ID: 65Z05
Mathematics Subject Classification ID: 76M99
zbMATH DE Number: 4001681
zbMATH Keywords: elastic bearing
zbMATH Keywords: non-Newtonian flow
zbMATH Keywords: Reynolds-Hertz equations
zbMATH Keywords: elastohydrodynamic lubrication
zbMATH Keywords: nonlinear variational inequality
zbMATH Keywords: exterior penalty method
zbMATH Keywords: convergence
zbMATH Keywords: finite element approximations
zbMATH Keywords: a priori error estimate
zbMATH Keywords: finite element solution
zbMATH Keywords: point contact problems
zbMATH Keywords: first-order convergence
zbMATH Keywords: pressure approximation
zbMATH Keywords: second-order convergence
MaRDI profile type: Publication
full work available at URL: 0898-1221(87)90119-2
OpenAlex ID: W2088478339
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published in: Computers & Mathematics with Applications
description: scientific article; zbMATH DE number 4001681