论文标题
STOKES方程的简单不合格的四面体元素
A simple nonconforming tetrahedral element for the Stokes equations
论文作者
论文摘要
在本文中，我们将不合格的旋转双线四面体元素应用于$ \ Mathbb {r}^3 $中的Stokes问题。我们表明该元件与压力的分段线性，连续的近似结合在一起。这给出了类似于众所周知的连续$ p^2-p^1 $ taylor $ - $ hood Element的近似值，但自由度较少。该元素是稳定的不合格低阶元素，可满足KORN的不平等，在stokes方程式以应力形式写入以供自由表面流动的情况下，也导致稳定性。
In this paper we apply a nonconforming rotated bilinear tetrahedral element to the Stokes problem in $\mathbb{R}^3$. We show that the element is stable in combination with a piecewise linear, continuous, approximation of the pressure. This gives an approximation similar to the well known continuous $P^2-P^1$ Taylor$-$Hood element, but with fewer degrees of freedom. The element is a stable non-conforming low order element which fulfils Korn's inequality, leading to stability also in the case where the Stokes equations are written on stress form for use in the case of free surface flow.
