Iterative solution techniques for the stokes and Navier‐Stokes equations
Iterative solution techniques for the stokes and Navier‐Stokes equations
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斯托克斯和纳维-斯托克斯方程的迭代求解技术
DOI：
10.1002/fld.1650190106
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发表时间：
1994
影响因子：
1.8
通讯作者：
A. Wathen
中科院分区：
文献类型：
--
作者：
A. Ramage;A. Wathen
总结：由NavierStokes方程和连续性方程的Lagrange-Galerkin混合有限元近似产生的线性系统是对称不定的，并且具有与由Stokes问题的混合有限元离散产生的系统相同的块结构。本文考虑了这类系统的迭代解，比较了不定矩阵的一级预条件共轭余量法和更传统的两级压力校正法的性能。文中给出了每种方法所涉及的工作量的渐近估计以及相关的数值实验结果。
SUMMARY The linear system arising from a Lagrange-Galerkin mixed finite element approximation of the NavierStokes and continuity equations is symmetric indefinite and has the same block structure as a system arising from a mixed finite element discretization of a Stokes problem. This paper considers the iterative solution of such a system, comparing the performance of the one-level preconditioned conjugate residual method for indefinite matrices with that of a more traditional two-level pressure correction approach. Asymptotic estimates for the amount of work involved in each method are given together with the results of related numerical experiments.