Continuous interior penalty stabilization for divergence-free finite element methods
Continuous interior penalty stabilization for divergence-free finite element methods
复制标题
无散有限元方法的连续内罚稳定
DOI：
10.1093/imanum/drad030
复制
发表时间：
2023
影响因子：
2.1
通讯作者：
Barrenechea G
中科院分区：
文献类型：
--
作者：
Barrenechea G
本文针对不可压缩流体力学中的一个线性化问题，即定常的低粘性Osee方程，提出了一种压力稳健稳定化有限元，并对其进行了数值分析和验证。稳定项是由对流项在区域三角剖分的单元面上的不同导数组合的跳跃定义的。借助于这些稳定项，并假定有限元空间提供一个逐点无散度的速度，证明了该方法(在对流占优区域)的-范数误差估计，以及误差剩余范数的最优阶估计。给出了支持理论结果的数值结果。
In this paper, we propose, analyze and test numerically a pressure-robust stabilized finite element for a linearized problem in incompressible fluid mechanics, namely, the steady Oseen equation with low viscosity. Stabilization terms are defined by jumps of different combinations of derivatives for the convective term over the element faces of the triangulation of the domain. With the help of these stabilizing terms, and the fact the finite element space is assumed to provide a point-wise divergence-free velocity, anerror estimate in the-norm is proved for the method (in the convection-dominated regime), and optimal order estimates in the remaining norms of the error. Numerical results supporting the theoretical findings are provided.