论文标题
无差异有限元方法的连续内部惩罚稳定
Continuous Interior Penalty stabilization for divergence-free finite element methods
论文作者
论文摘要
在本文中，我们在数值上提出，分析和测试了不可压缩流体力学中线性化问题的压力稳定有限元，即，稳定的OSEEN方程低粘度。稳定项是由对流项的不同组合在域的三角元素面上的元素面上的跳跃来定义的。借助这些稳定术语，以及假定有限的元素空间可以提供无点的无分流速度，一个$ \ Mathcal o \ big（h^{k+\ frac12} \ big）$错误估计在$ l^2 $中的$ l^2 $中的错误估计是为了使该方法的估算（在对符号范围内的算法），并在依次进行了序列中，并依次进行了依次的序列，并估算了依次的指定。提供了支持理论发现的数值结果。
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, an $\mathcal O\big(h^{k+\frac12}\big)$ error estimate in the $L^2$-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.
