PENALTY APPROXIMATION OF STOKES-FLOW
PENALTY APPROXIMATION OF STOKES-FLOW
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DOI：
10.1016/0045-7825(82)90133-5
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发表时间：
1982-01-01
影响因子：
7.2
通讯作者：
KRISHNAN, R
中科院分区：
文献类型：
--
作者：
CAREY, GF;KRISHNAN, R
所考虑的特殊问题是Stokes流，其中的约束条件是速度场上的不可压缩性条件μ·u= 0。在第一部分中，我们首先提出了一种确定寄生模式的简单的构造性方法。其次是分析的离散稳定性条件的惩罚方法，表明该条件与一个参数是O（h）。我们开发了改进的估计的稳定性参数的依赖网格sizehin一个更一般的证明比以前available.In第二部分，我们证明了误差估计的速度和计算的压力近似，并使用Aubin-Nitsche技术getL 2估计的速度。在最后的数值研究中，我们研究了具有不同规律性的数据的问题的计算压力和收敛速度的稳定性。
The particular class of problems considered is Stokes flow in which the constraint is the incompressibility condition ▽ ·u= 0 on the velocity fieldu. In Part I we present first of all a simple constructive method for determining the spurious modes. This is followed by an analysis of the discrete stability condition for the penalty method, showing that this condition holds with a parameter that is O(h). We develop improved estimates of the dependence of the stability parameter on mesh sizehin a more general proof than previously available.In Part II we prove error estimates for the velocity and computed pressure approximations and use an Aubin-Nitsche technique to getL2estimates for the velocity. In the concluding numerical studies we examine the stability of the computed pressure and convergence rates with uniform mesh refinement for problems having data with varying degree of regularity.