TY - JOUR
T1 - Interior-Exterior Penalty Approach for Solving Elasto-Hydrodynamic Lubrication Problem: Part I
AU - Singh , Peeyush
AU - Sinha , Prawal
JO - International Journal of Numerical Analysis and Modeling
VL - 5
SP - 695
EP - 731
PY - 2020
DA - 2020/08
SN - 17
DO - http://doi.org/
UR - https://global-sci.org/intro/article_detail/ijnam/17879.html
KW - Elasto-hydrodynamic lubrication, discontinuous finite volume method, interior-exterior penalty method, pseudo-monotone operators, variational inequality.
AB - <p style="text-align: justify;">A new interior-exterior penalty method for solving quasi-variational inequality and
pseudo-monotone operator arising in two-dimensional point contact problem is analyzed and developed in discontinuous Galerkin finite volume (DG-FVEM) framework. We derive a discrete
DG-FVEM formulation of the problem and prove existence and uniqueness results for it. Optimal
error estimates in $H^1$&nbsp;and $L^2$&nbsp;norm are derived under a light load parameter assumptions. In
addition, the article provides a complete algorithm to tackle all numerical complexities appear in
the solution procedure. Numerical outcomes are presented for light, moderate and relative high
load conditions. The variations of load parameter and its effect on the evolution of deformations
and pressure profile are evaluated and described. This method is well suited for solving elasto-hydrodynamic lubrication point contact problems and can probably be treated as commercial
software. Furthermore, the results give a hope for the further development of the scheme for
extreme load condition, observations in a more realistic operating situation which will be discussed in
part II.</p>