Year: 2020
Author: Peeyush Singh, Prawal Sinha
International Journal of Numerical Analysis and Modeling, Vol. 17 (2020), Iss. 5 : pp. 695–731
Abstract
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 $H^1$ and $L^2$ 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.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/2020-IJNAM-17879
International Journal of Numerical Analysis and Modeling, Vol. 17 (2020), Iss. 5 : pp. 695–731
Published online: 2020-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 37
Keywords: Elasto-hydrodynamic lubrication discontinuous finite volume method interior-exterior penalty method pseudo-monotone operators variational inequality.