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Volume 25, Issue 3
The Generalized Arrow-Hurwicz Method with Applications to Fluid Computation

Binbin Du & Jianguo Huang

DOI: 10.4208/cicp.OA-2017-0235

Commun. Comput. Phys., 25 (2019), pp. 752-780.

Published online: 2018-11

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  • Abstract

In this paper, we first discuss the existence and uniqueness of a class of nonlinear saddle-point problems, which are frequently encountered in physical models. Then, a generalized Arrow-Hurwicz method is introduced to solve such problems. For the method, the convergence rate analysis is established under some reasonable conditions. It is also applied to solve three typical discrete methods in fluid computation, with the computational efficiency demonstrated by a series of numerical experiments.

  • Keywords

Nonlinear saddle-point problems, the generalized Arrow-Hurwicz method, convergence rate analysis, fluid computation.

  • AMS Subject Headings

65N30, 65N22, 75D05

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{CiCP-25-752, author = {Binbin Du and Jianguo Huang}, title = {The Generalized Arrow-Hurwicz Method with Applications to Fluid Computation}, journal = {Communications in Computational Physics}, year = {2018}, volume = {25}, number = {3}, pages = {752--780}, abstract = {

In this paper, we first discuss the existence and uniqueness of a class of nonlinear saddle-point problems, which are frequently encountered in physical models. Then, a generalized Arrow-Hurwicz method is introduced to solve such problems. For the method, the convergence rate analysis is established under some reasonable conditions. It is also applied to solve three typical discrete methods in fluid computation, with the computational efficiency demonstrated by a series of numerical experiments.

}, issn = {1991-7120}, doi = {https://doi.org/10.4208/cicp.OA-2017-0235}, url = {http://global-sci.org/intro/article_detail/cicp/12828.html} }
TY - JOUR T1 - The Generalized Arrow-Hurwicz Method with Applications to Fluid Computation AU - Binbin Du & Jianguo Huang JO - Communications in Computational Physics VL - 3 SP - 752 EP - 780 PY - 2018 DA - 2018/11 SN - 25 DO - http://doi.org/10.4208/cicp.OA-2017-0235 UR - https://global-sci.org/intro/article_detail/cicp/12828.html KW - Nonlinear saddle-point problems, the generalized Arrow-Hurwicz method, convergence rate analysis, fluid computation. AB -

In this paper, we first discuss the existence and uniqueness of a class of nonlinear saddle-point problems, which are frequently encountered in physical models. Then, a generalized Arrow-Hurwicz method is introduced to solve such problems. For the method, the convergence rate analysis is established under some reasonable conditions. It is also applied to solve three typical discrete methods in fluid computation, with the computational efficiency demonstrated by a series of numerical experiments.

Binbin Du and Jianguo Huang. (2018). The Generalized Arrow-Hurwicz Method with Applications to Fluid Computation. Communications in Computational Physics. 25 (3). 752-780. doi:10.4208/cicp.OA-2017-0235
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