A lowest-order weak Galerkin finite element method for Stokes flow on polygonal meshes
A lowest-order weak Galerkin finite element method for Stokes flow on polygonal meshes
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DOI：
10.1016/j.cam.2019.112479
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发表时间：
2020-04
期刊：
影响因子：
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通讯作者：
Jiangguo Liu;Graham Harper;Nolisa S. Malluwawadu;S. Tavener
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文献类型：
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作者：
Jiangguo Liu;Graham Harper;Nolisa S. Malluwawadu;S. Tavener
提出了一种在凸多边形网格上求解Stokes方程的最低阶弱Galerkin（WG）有限元方法。常数矢量分别用于元素内部和边缘以近似流体速度，而常数标量用于元素以近似压力。对于常数向量基函数，它们的离散弱梯度是在基于C W 0空间的矩阵空间中建立的（Chen和Wang，2017），而它们的离散弱发散是作为元素常数计算的。为了避免鞍点问题，在离散无发散子空间中，采用三种基函数建立了速度的简化格式。还开发了后续压力恢复的程序。误差分析沿着与基准上的数值实验，以证明所提出的新方法的精度和效率。
This paper presents a lowest-order weak Galerkin (WG) finite element method for solving the Stokes equations on convex polygonal meshes. Constant vectors are used separately in element interiors and on edges to approximate fluid velocity, whereas constant scalars are used on elements to approximate the pressure. For the constant vector basis functions, their discrete weak gradients are established in a matrix space that is based on the C W 0 space (Chen and Wang, 2017), whereas their discrete weak divergences are calculated as elementwise constants. To circumvent the saddle-point problem, a reduced scheme for velocity is established by using three types of basis functions for the discretely divergence-free subspace. A procedure for subsequent pressure recovery is also developed. Error analysis along with numerical experiments on benchmarks are presented to demonstrate accuracy and efficiency of the proposed new method.