论文标题
用于Stokes方程的低成本，无参数和压力量富集的Galerkin方法
A low-cost, parameter-free, and pressure-robust enriched Galerkin method for the Stokes equations
论文作者
论文摘要
在本文中，我们根据具有不连续速度富集函数的富集盖尔金（EG）方法提出了一种低成本，无参数和压力的stokes solver求解器。 EG方法采用内部惩罚不连续的Galerkin（IPDG）制剂来弱施加速度函数的连续性。但是，对称IPDG公式尽管具有对称性的优势，但仍需要大量的计算努力来选择最佳的惩罚参数并计算不同的跟踪项。为了减少这种努力，我们用元素的几何数据计算出的弱衍生物代替了速度函数的衍生物。因此，我们修改的EG（MEG）方法是一种无参数的数值方案，它降低了计算复杂性和最佳收敛速率。此外，我们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MEG方法的压力量。通过具有二维和三维示例的数值实验证实了理论结果。
In this paper, we propose a low-cost, parameter-free, and pressure-robust Stokes solver based on the enriched Galerkin (EG) method with a discontinuous velocity enrichment function. The EG method employs the interior penalty discontinuous Galerkin (IPDG) formulation to weakly impose the continuity of the velocity function. However, the symmetric IPDG formulation, despite of its advantage of symmetry, requires a lot of computational effort to choose an optimal penalty parameter and to compute different trace terms. In order to reduce such effort, we replace the derivatives of the velocity function with its weak derivatives computed by the geometric data of elements. Therefore, our modified EG (mEG) method is a parameter-free numerical scheme which has reduced computational complexity as well as optimal rates of convergence. Moreover, we achieve pressure-robustness for the mEG method by employing a velocity reconstruction operator on the load vector on the right-hand side of the discrete system. The theoretical results are confirmed through numerical experiments with two- and three-dimensional examples.
