内-外惩罚方法用于求解弹性流体动力润滑问题：第一部分
Interior-exterior penalty approach for solving elasto-hydrodynamic lubrication problem: Part I
AI总结：
本文提出了一种新的内-外惩罚方法，用于求解二维点接触问题中出现的准变分不等式和伪单调算子，无需对润滑剂的粘度或密度进行任何常数假设，实现了H¹和L²范数的最佳误差估计，并提供了一个完整的算法来处理求解过程中的所有数值复杂性。
摘要：
本文提出了一种新的内-外惩罚方法，用于求解准变分不等式和伪单调算子，这些算子出现在二维点接触问题中。在间断有限体积法环境下，该方法已被分析和开发。本文证明了在不假设润滑剂粘度或密度常数的情况下，更现实的模型问题解的存在性。我们展示了在轻载无量纲参数条件下，H¹和L²范数的最佳误差估计可以实现。此外，我们提供了一个完整的算法来处理求解过程中出现的所有数值复杂性。我们得到了中等负载条件下的结果，并在本节末尾进行了讨论。此外，这些结果为未来在更现实的运行条件下开发该方案以处理高负载条件提供了希望，这将在第二部分中讨论。该方法适用于求解弹性流体动力润滑线以及点接触问题，并可能被视作商业软件。
英文摘要：
A new interior-exterior penalty method for solving quasi-variational inequality and pseudo-monotone operators arising in two-dimensional point contact problem has been analyzed and developed in discontinuous Galerkin finite volume method environment. In this article, we proved the existence of solution for the more realistic model problem without taking any constant assumption in viscosity or density of the lubricant. We have shown that optimal error estimate of $H^{1}$ and $L^{2}$ norm can be achieved under a light load non-dimensional parameter condition. In addition, we provided a complete algorithm to tackle all numerical complexities appear in the solution procedure. We obtained results for moderate loaded conditions which have been discussed at the end of the section. Furthermore, results give a hope for the further development of the scheme for highly loaded condition appeared in a more realistic operating situation which will be discussed in part II. This method is well suited for solving elasto-hydrodynamic lubrication line as well as point contact problems and can probably be treated as commercial software.
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