论文标题
使用内部惩罚方法对弹性流动力润滑的先验误差估计
A priori error estimation for elasto-hydrodynamic lubrication using interior-exterior penalty approach
论文作者
论文摘要
在本研究中，分析了内部外部惩罚不连续的盖金有限元法（DG-FEM），以求解弹性流体动力润滑（EHL）线和点接触问题。使用Brouwer的固定点定理检查离散惩罚解决方案的存在。此外，在光负载参数假设下，使用离散解决方案图的Lipschitz连续性证明了解决方案的唯一性。在$ l^{2} $和$ h^{1} $ norms中实现了先验错误估计，这些估计值在网格尺寸$ h $中是最佳的，而多项式度$ p $ subiptimal。理论发现的有效性通过一系列数值实验证实。
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.
