具有滑动边界条件Stokes问题的自适应Uzawa块松弛算法

对一类具有非线性滑动边界条件的Stokes问题，得到了求其数值解的自适应Uzawa块松弛算法（SUBRM）.通过该问题导出的变分问题，引入辅助变量将原问题转化为一个基于增广Lagrange函数表示的鞍点问题，并采用Uzawa块松弛算法（UBRM）求解.为了提高算法性能，提出利用迭代函数自动选取合适罚参数的自适应法则.该算法的优点是每次迭代只需计算一个线性问题，同时显式计算辅助变量.对算法的收敛性进行了理论分析，最后用数值结果验证了该算法的可行性和有效性.

A Self-Adaptive Uzawa Block Relaxation Method for Stokes Problems With Slip Boundary Conditions

A self-adaptive Uzawa block relaxation method was designed for Stokes problems under nonlinear slip boundary conditions. For the variational formulation of the problem, an auxiliary unknown was introduced to transform the problem into a saddle-point one based on an augmented Lagrangian function, which can be solved with the Uzawa block relaxation method. To improve the performance of the method, a self-adaptive rule was proposed with the proper penalty parameter chosen automatically. The main advantage of this method is that each iterative step consists of a linear problem while the auxiliary unknown can be computed explicitly. The convergence of the algorithm was analyzed. The numerical results show the feasibility and effectiveness of the proposed method.