Convergence of Regularized Time-Stepping Methods for Differential Variational Inequalities
Convergence of Regularized Time-Stepping Methods for Differential Variational Inequalities
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DOI：
10.1137/120875223
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发表时间：
2013-08
期刊：
影响因子：
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通讯作者：
Xiaojun Chen;Zhengyu Wang
中科院分区：
文献类型：
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作者：
Xiaojun Chen;Zhengyu Wang
本文给出了求解微分变分不等式（DVI）问题的正则化时步方法的收敛性分析，该问题由一个常微分方程组和一个参数变分不等式（PVI）约束组成. PVI问题在时步法的每一步往往存在多个解，难以选择合适的解来保证收敛性。在[L. Han，A.蒂瓦里，M。K. Camlibel和J. - S. Pang，SIAM J. Numer.分析：47（2009）pp. 3768- 3796]中，提出了在单调线性互补系统的时间步方法的每一步中使用参数线性互补问题的“最小范数解”，并说明了使用最小范数解的新奇和优越性.然而，在数值实现中，当PVI不是单调的，它的解集不是凸的，找到一个最小范数的解决方案是困难的。本文将Tikhonov正则化逼近推广到P0-函数DVI上，使其具有更好的收敛性。
This paper provides convergence analysis of regularized time-stepping methods for the differential variational inequality (DVI), which consists of a system of ordinary differential equations and a parametric variational inequality (PVI) as the constraint. The PVI often has multiple solutions at each step of a time-stepping method, and it is hard to choose an appropriate solution for guaranteeing the convergence. In [L. Han, A. Tiwari, M. K. Camlibel and J.-S. Pang, SIAM J. Numer. Anal., 47 (2009) pp. 3768--3796], the authors proposed to use “least-norm solutions” of parametric linear complementarity problems at each step of the time-stepping method for the monotone linear complementarity system and showed the novelty and advantages of the use of the least-norm solutions. However, in numerical implementation, when the PVI is not monotone and its solution set is not convex, finding a least-norm solution is difficult. This paper extends the Tikhonov regularization approximation to the P$_0$-function DVI, whi...