求解具有泄漏边界条件Stokes问题的Uzawa迭代算法

Uzawa Iterative Algorithm for Solving Stokes Problem with Leak Boundary Conditions

【目的】为了数值求解非线性泄漏边界条件下的Stokes问题,得到Uzawa迭代算法。【方法】引入一个凸集中的拉格朗日乘子,使得该问题的变分不等式等价于一个变分等式,且变分等式的解满足一个用拉格朗日函数表示的鞍点问题,并采用Uzawa迭代算法求解鞍点问题。【结果】对算法进行了收敛性分析,得到了收敛率结果。【结论】数值结果验证了Uzawa迭代算法的可行性。

[Purposes]A Uzawa iterative algorithm is proposed to solve Stokes problem under nonlinear leak boundary conditions.[Methods]A multiplier in a convex set is introduced such that the variational inequality is equivalent to the variational identity,and the solution of the variational identity satisfies the saddle point problem of Lagrangian function.The Uzawa iterative algorithm is proposed to solve the saddle point problem.[Findings]The convergence of the algorithm is proved and the convergence rate is obtained.[Conclusions]Numerical results verify the feasibility of Uzawa iterative algorithm.