Abstract
Based on full domain partition, three parallel iterative finite-element algorithms are proposed and analyzed for the Navier–Stokes equations with nonlinear slip boundary conditions. Since the nonlinear slip boundary conditions include the subdifferential property, the variational formulation of these equations is variational inequalities of the second kind. In these parallel algorithms, each subproblem is defined on a global composite mesh that is fine with size h on its subdomain and coarse with size H (H ≫ h) far away from the subdomain, and then we can solve it in parallel with other subproblems by using an existing sequential solver without extensive recoding. All of the subproblems are nonlinear and are independently solved by three kinds of iterative methods. Compared with the corresponding serial iterative finite-element algorithms, the parallel algorithms proposed in this paper can yield an approximate solution with a comparable accuracy and a substantial decrease in computational time. Contributions of this paper are as follows: (1) new parallel algorithms based on full domain partition are proposed for the Navier–Stokes equations with nonlinear slip boundary conditions; (2) nonlinear iterative methods are studied in the parallel algorithms; (3) new theoretical results about the stability, convergence and error estimates of the developed algorithms are obtained; (4) some numerical results are given to illustrate the promise of the developed algorithms.
Funding source: the Basic and Frontier Explore Program of Chongqing Municipality, China
Award Identifier / Grant number: cstc2018jcyjAX0305
Funding source: Fundamental Research Funds for the Central Universities
Award Identifier / Grant number: XDJK2018B032
Funding source: National Natural Science Foundation of China
Award Identifier / Grant number: 11361016
Acknowledgments
The authors appreciate the valuable comments and suggestions made by the reviewers which led to an improvement of the paper.
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Author contribution: All the authors have accepted responsibility for the entire content of this submitted manuscript and approved submission.
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Research funding: This work was supported by the Natural Science Foundation of China (No. 11361016), the Basic and Frontier Explore Program of Chongqing Municipality, China (No. cstc2018jcyjAX0305), and Fundamental Research Funds for the Central Universities (No. XDJK2018B032).
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Conflict of interest statement: The authors declare no conflicts of interest.
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