Convergence and error estimates for finite element solutions of elastohydrodynamic lubrication
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.
scientific article; zbMATH DE number 4001681