Volume 42 Issue 2
Feb.  2021
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Article Contents
ZHANG Maolin, RAN Jing, ZHANG Shougui. A Self-Adaptive Uzawa Block Relaxation Method for Stokes Problems With Slip Boundary Conditions[J]. Applied Mathematics and Mechanics, 2021, 42(2): 188-198. doi: 10.21656/1000-0887.410170
 Citation: ZHANG Maolin, RAN Jing, ZHANG Shougui. A Self-Adaptive Uzawa Block Relaxation Method for Stokes Problems With Slip Boundary Conditions[J]. Applied Mathematics and Mechanics, 2021, 42(2): 188-198.

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

##### doi: 10.21656/1000-0887.410170
Funds:  The National Natural Science Foundation of China（11971085）
• Rev Recd Date: 2020-07-25
• Publish Date: 2021-02-01
• 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.
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