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

ZHANG Maolin; RAN Jing; ZHANG Shougui

doi:10.21656/1000-0887.410170

Volume 42 Issue 2

Feb. 2021

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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

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

doi: 10.21656/1000-0887.410170

School of Mathematical Sciences, Chongqing Normal University, Chongqing 401331, P.R.China

Funds: The National Natural Science Foundation of China（11971085）

Received Date: 2020-06-11
Rev Recd Date: 2020-07-25
Publish Date: 2021-02-01

Abstract

Abstract

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.
- Stokes problem,
- slip boundary,
- Uzawa block relaxation method,
- self-adaptive rule,
- augmented Lagrangian function

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References(17)

References

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