论文标题
分析一类全球无差异HDG方法用于固定Navier-Stokes方程
Analysis of a class of globally divergence-free HDG methods for stationary Navier-Stokes equations
论文作者
论文摘要
本文分析了一类无差异（以及因此压力）杂交不连续的盖尔金（HDG）有限元方法的固定纳维尔 - 斯托克斯方程的有限元方法。该方法使用$ \ MATHCAL {p} _ {k}/\ MATHCAL {P} _ {K-1} $（K \ GEQ1）$不连续的有限元组合，用于元素内部的速度和压力近似，以及元素内部的压力近似值，以及零件$ \ nathcal $ \ nathcal} $ {对于速度和元素间边界上的压力的迹线。结果表明，对于连续解决方案的唯一条件，可以用足够小的网格尺寸来保证它的唯一条件。基于派生的离散HDG Sobolev嵌入性能，获得了最佳误差估计。进行数值实验以验证理论分析。
This paper analyzes a class of globally divergence-free (and therefore pressure-robust) hybridizable discontinuous Galerkin (HDG) finite element methods for stationary Navier-Stokes equations. The methods use the $\mathcal{P}_{k}/\mathcal{P}_{k-1}$ $(k\geq1)$ discontinuous finite element combination for the velocity and pressure approximations in the interior of elements, and piecewise $\mathcal{P}_k/\mathcal{P}_{k}$ for the trace approximations of the velocity and pressure on the inter-element boundaries. It is shown that the uniqueness condition for the discrete solution is guaranteed by that for the continuous solution together with a sufficiently small mesh size. Based on the derived discrete HDG Sobolev embedding properties, optimal error estimates are obtained. Numerical experiments are performed to verify the theoretical analysis.
