Numerical Analysis of a Frictional Problem Using the Parabolic Variational Inequalities
Numerical method of a frictional Problem using the parabolic variational inequalities is discussed. The equation of the frictional problem is given, then we obtain the parabolic variatinal inequaities of the second kind which is equivalent the frictional problem. The traditional idea to solve the variational inequalities is direct study of the original variational inequality. But the parabolic variational inequality of the second kind is difficult to solve directly because the time derivative term and the non-differentiable term. In view of the above difficulties we introduce a relaxation algorithm in this paper. Firstly, the parabolic variational inequalities of the second kind can be reduced to an elliptic vatiational inequality by using semi-discretization and implicit method in time, then we reduce the equivalent optimization problem. Secondly, we use numerical integration approximation the non-differentiable item and discrete the optimization problem by finite element method. Next, the relaxation algorithm is given and the convergence of the relaxation algorithm is proved. Finally, the given example proves that the algorithm is effectiveness and feasibility.
Frictional problem Parabolic variational inequalities Numerical integration Finite element method Relazation algorithm
FENG Bin CHEN Yi-ming SHEN Guangxian ZhaoWanshuai LI Hai-hua
College of Sciences,Yanshan University,Qinhuangdao,Hebei 066004,China
国际会议
南京
英文
1
2009-10-18（万方平台首次上网日期，不代表论文的发表时间）