In this work, we are mainly interested in modelling a particular lubrication regime known as Elastohydrodynamic (EHD). The pressure generated in the conjunction is high enough to induce a significant elastic deformation of the contacting bodies. Therefore a strong coupling between hydrodynamic and elastic effects is involved. A finite element full-system approach is used to model the lubricant ...

Over the last few years, several mixed discontinuous Galerkin finite element methods (DGFEM) have been proposed for the discretization of incompressible fluid flow problems. We mention here only the piecewise solenoidal discontinuous Galerkin methods introduced in [5,25], the local discontinuous Galerkin methods of [12,11], and the interior penalty methods studied in [24,33,18]. Some of the mai...

In this paper we analyze local properties of the Continuous Interior Penalty (CIP) Method for a model convection-dominated singularly perturbed convection-diffusion problem. We show weighted a priori error estimates, where the weight function exponentially decays outside the subdomain of interest. This result shows that locally, the CIP method is comparable to the Streamline Diffusion (SD) or t...

where gh is an approximation of g and V 0 h ⊂ H 1 0 (Ω) is a finite element subspace. In practice, gh is considered to be a nodal interpolation of g in Vh|∂Ω, where Vh ⊂ H(Ω) is a finite element subspace. However it is shown in [4] that the error estimates for (3) are better when gh is chosen to be the L2-projection of g onto Vh|∂Ω. In particular when gh is chosen to be a nodal interpolation, t...