  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.
