论文标题
Stokes方程的压力量富集的Galerkin方法
Pressure-robust enriched Galerkin methods for the Stokes equations
论文作者
论文摘要
In this paper, we present a pressure-robust enriched Galerkin (EG) scheme for solving the Stokes equations, which is an enhanced version of the EG scheme for the Stokes problem proposed in [Son-Young Yi, Xiaozhe Hu, Sanghyun Lee, James H. Adler, An enriched Galerkin method for the Stokes equations, Computers and Mathematics with Applications, accepted, 2022].通过在离散系统右侧的负载向量上使用速度重建算子来实现压力量。先验误差分析证明，速度误差与压力和粘度无关。我们还提出和分析了压力射击方法的扰动版本，该版本允许消除通过静态凝结与速度矢量不连续的组件相对应的自由度。结果方法可以看作是稳定的$ h^1 $ - 符合$ \ mathbb {p} _1 $ - $ \ mathbb {p} _0 $方法。此外，我们考虑了其性能独立于粘度的有效块预处理。理论结果通过两个维度和三个维度的各种数值实验证实。
In this paper, we present a pressure-robust enriched Galerkin (EG) scheme for solving the Stokes equations, which is an enhanced version of the EG scheme for the Stokes problem proposed in [Son-Young Yi, Xiaozhe Hu, Sanghyun Lee, James H. Adler, An enriched Galerkin method for the Stokes equations, Computers and Mathematics with Applications, accepted, 2022]. The pressure-robustness is achieved by employing a velocity reconstruction operator on the load vector on the right-hand side of the discrete system. An a priori error analysis proves that the velocity error is independent of the pressure and viscosity. We also propose and analyze a perturbed version of our pressure-robust EG method that allows for the elimination of the degrees of freedom corresponding to the discontinuous component of the velocity vector via static condensation. The resulting method can be viewed as a stabilized $H^1$-conforming $\mathbb{P}_1$-$\mathbb{P}_0$ method. Further, we consider efficient block preconditioners whose performances are independent of the viscosity. The theoretical results are confirmed through various numerical experiments in two and three dimensions.
