自适应梯度分割参数选择

摘要：

我们提出，分析和测试一个新的自适应惩罚计划，挑选罚参数$ε$元素小的地方$\nabla\cdot u^h$是大的。我们首先分析和测试的新计划最简单但有趣的设置，斯托克斯问题。最后，我们将该算法推广到不可压Navier斯托克斯方程的复杂流动问题，并进行了验证。实验表明，新的自适应$ε$罚函数算法能够准确地预测流场特性.该方案是在惩罚方法中开发的，但也可以用于选择梯度-梯度稳定参数。

英文摘要：

We propose, analyze and test a new adaptive penalty scheme that picks the penalty parameter $ε$ element by element small where $\nabla\cdot u^h$ is large. We start by analyzing and testing the new scheme on the most simple but interesting setting, the Stokes problem. Finally, we extend and test the algorithm on the incompressible Navier Stokes equation on complex flow problems. Tests indicate that the new adaptive-$ε$ penalty method algorithm predicts flow behavior accurately. The scheme is developed in the penalty method but also can be used to pick a grad-div stabilization parameter.

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