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# A Domain Decomposition Method Based on Natural BEM and Mixed FEM for Stationary Stokes Equations on Unbounded Domains

Ju’e Yang1, Hongying Huang2, Dehao Yu3
School of Mathematics and Statistics, Lanzhou University, Lanzhou 730000, China(yangje@lzu.edu.cn).
School of Mathematics, Physics and Information Science, Zhejiang Ocean University, Zhoushan, Zhejiang, 316004, China(huanghy@lsec.cc.ac.cn).
School of Mathematical Sciences, Xiamen University, Xiamen 361005, and Academy of Mathematics and System Science, CAS, Beijing 100190, China(ydh@lsec.cc.ac.cn).

Computer Modeling in Engineering & Sciences 2012, 85(4), 347-366. https://doi.org/10.3970/cmes.2012.085.347

### Abstract

In this paper, a new domain decomposition method is suggested for the stationary Stokes equations on unbounded domain and its convergence is proved. We draw an artificial boundary to make the domain into two parts: one is bounded, in which we use the mixed finite element method; the other is unbounded, in which we apply the natural boundary reduction. Then we change the sub-problem on the unbounded domain onto a one in a bounded domain and we use the Dirichlet to Neumann(DtN) alternating algorithm to solve the resulting mixed system. The theoretical results as well as the numerical examples show that this method is very effective especially for problems over unbounded domains.

### Keywords

Yang, J., Huang, H., Yu, D. (2012). A Domain Decomposition Method Based on Natural BEM and Mixed FEM for Stationary Stokes Equations on Unbounded Domains. CMES-Computer Modeling in Engineering & Sciences, 85(4), 347–366.

This work is licensed under a Creative Commons Attribution 4.0 International License , which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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