Analysis and convergence of a covolume method for the generalized Stokes problem
Analysis and convergence of a covolume method for the generalized Stokes problem
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DOI：
10.1090/s0025-5718-97-00792-8
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发表时间：
1997
期刊：
影响因子：
--
通讯作者：
S. Chou
中科院分区：
文献类型：
--
作者：
S. Chou
我们引入一个covolume或MAC类方法近似广义Stokes问题。在离散化中需要两个网格：三角形网格用于连续性方程，四边形网格用于动量方程。速度采用分段线性近似，压力采用分段常数近似。误差的L2范数的压力和误差的网格依赖H1范数以及在L2范数的速度被证明是一阶的，提供的确切速度是在H2和H I的真实压力。我们还引入了一个网络模型的概念到离散化的线性系统，使一个有效的压力恢复技术可以用来简化了大量的增广拉格朗日方法所涉及的计算工作。给出了一个非常一般的分解条件，在此条件下，该方法也适用于其它可表述为鞍点问题的流体问题。
We introduce a covolume or MAC-like method for approximating the generalized Stokes problem. Two grids are needed in the discretization; a triangular one for the contimlity equation and a quadrilateral one for the momentum equation. The velocity is approximated using nonconforming piecewise linears and the pressure piecewise constants. Error in the L 2 norm for the pressure and error in a mesh dependent H 1 norm as well as in the L 2 norm for the velocity are shown to be of first order, provided that the exact velocity is in H 2 and the true pressure in H I . We also introduce the concept of a network model into the discretized linear system so that an efficient pressure-recovering technique can be used to simplify a great deal the computational work involved in the augmented Lagrangian method. Given is a very general decomposition condition under which this technique is applicable to other fluid problems that can be formulated as a saddle-point problem.