论文标题
Stokes方程的无稳定器有限元法
A stabilizer-free pressure-robust finite element method for the Stokes equations
论文作者
论文摘要
在本文中，我们引入了一种新的有限元方法，用于求解主要速度压力公式中的Stokes方程。该方法采用$ h（div）$有限元素来近似速度，这带来了两个独特的优势：精确的无差异速度场和压力稳定性。此外，该方法具有简单的公式，而没有任何稳定器或罚款。在各种规范中为相应的数值近似建立了最佳订单误差估计。进行了广泛的数值研究以检验该方法的准确性和鲁棒性并确认理论。数值示例涵盖了高度和高级近似值，直至第四度以及2D和3D病例。
In this paper, we introduce a new finite element method for solving the Stokes equations in the primary velocity-pressure formulation. This method employs $H(div)$ finite elements to approximate velocity, which leads to two unique advantages: exact divergence free velocity field and pressure-robustness. In addition, this method has a simple formulation without any stabilizer or penalty term. Optimal-order error estimates are established for the corresponding numerical approximation in various norms. Extensive numerical investigations are conducted to test accuracy and robustness of the method and to confirm the theory. The numerical examples cover low and high order approximations up to the degree four, and 2D and 3D cases.
