| 关于Stokes和线性Navier-Stokes方程的广义维数分裂迭代方法 |
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| 引用本文： | 潘春平. 关于Stokes和线性Navier-Stokes方程的广义维数分裂迭代方法[J]. 计算数学, 2014, 36(3): 231-244 |
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| 作者姓名： | 潘春平 |
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| 作者单位： | 浙江工业职业技术学院, 浙江绍兴 312000 |
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| 基金项目： | 浙江省教育厅科研项目资助(Y201432547);全国教育信息技术研究课题(126240641);浙江省高职研究会课题(YB1115);浙江工业职业技术学院科技计划项目(1023401092012014) |
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| 摘 要： | 本文研究了鞍点问题的迭代法.在Benzi等人提出的维数分裂(DS)迭代方法的基础上,提出了具有三个参数的广义维数分裂(GDS)迭代法,该方法包含了DS迭代法,理论分析表明该方法是无条件收敛的.通过对有限差分法和有限元法离散的Stokes问题及有限元法离散的Oseen问题的数值结果表明,本文所给方法是有效的.
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| 关 键 词： | 鞍点问题 迭代法 维数分裂 Stokes问题 Oseen问题 |
| 收稿时间： | 2013-08-01; |
ON GENERALIZED DIMENSIONAL SPLITTING ITERATIVEMETHODS FOR STOKES AND LINEARIZED NAVIER-STOKES EQUATIONS |
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| Pan Chunping. ON GENERALIZED DIMENSIONAL SPLITTING ITERATIVEMETHODS FOR STOKES AND LINEARIZED NAVIER-STOKES EQUATIONS[J]. Mathematica Numerica Sinica, 2014, 36(3): 231-244 |
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| Authors: | Pan Chunping |
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| Affiliation: | Zhejiang Industry Polytechnic College, Shaoxing 312000, Zhejiang, China |
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| Abstract: | In this paper, we study the iterative methods for saddle point problems (SPP). Based on the dimensional splitting(DS) which was proposed by Benzi et al., we present a generalized dimensional splitting(GDS) iterative methods with three parameters which cover DS methods. Theoretical analysis shows that the new method is unconditional convergence. Numerical results from discrete Stokes problems by finite difference methods and finite element methods, and discrete Oseen problems by finite element methods show that the new method is efficient. |
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| Keywords: | Saddle-point problems iterative methods dimensional splitting Stokes problem Oseen problem |
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