论文标题
依赖历史的变异 - 杀菌性不平等的数值分析
Numerical Analysis of History-dependent Variational-hemivariational Inequalities
论文作者
论文摘要
在本文中，在接触问题中引起的一类历史依赖性变异性不平等现象进行了数值分析。提出了三种用于时间离散化的数值处理，以近似连续模型。使用定点迭代算法来实施隐式方案，并以收敛速率与时间尺寸和网格网格大小的收敛速率证明。引入了与历史有关的操作员引入特殊的时间离散化，从而导致数值方案可以证明时间离散系统的唯一可溶性和误差界限，而无需任何限制时间步长。至于空间近似，应用有限元方法，并在适当的规律性假设下提供了线性元素解决方案的最佳订单误差估计。提出了数值示例以说明理论结果。
In this paper, numerical analysis is carried out for a class of history-dependent variational-hemivariational inequalities arising in contact problems. Three different numerical treatments for temporal discretization are proposed to approximate the continuous model. Fixed-point iteration algorithms are employed to implement the implicit scheme and the convergence is proved with a convergence rate independent of the time step-size and mesh grid-size. A special temporal discretization is introduced for the history-dependent operator, leading to numerical schemes for which the unique solvability and error bounds for the temporally discrete systems can be proved without any restriction on the time step-size. As for spatial approximation, the finite element method is applied and an optimal order error estimate for the linear element solutions is provided under appropriate regularity assumptions. Numerical examples are presented to illustrate the theoretical results.
