数学
离散化
分段
分段线性函数
间断伽辽金法
伽辽金法
稳健性(进化)
数学分析
应用数学
线性系统
有限元法
收敛速度
基函数
常量(计算机编程)
常数函数
物理
频道(广播)
工程类
电气工程
基因
热力学
化学
生物化学
程序设计语言
计算机科学
作者
Son-Young Yi,Xiaozhe Hu,Sanghyun Lee,James H. Adler,Ludmil T. Zikatanov
标识
DOI:10.1016/j.camwa.2022.06.018
摘要
We present a new enriched Galerkin (EG) scheme for the Stokes equations based on piecewise linear elements for the velocity unknowns and piecewise constant elements for the pressure. The proposed EG method augments the conforming piecewise linear space for velocity by adding an additional degree of freedom which corresponds to one discontinuous linear basis function per element. Thus, the total number of degrees of freedom is significantly reduced in comparison with standard conforming, non-conforming, and discontinuous Galerkin schemes for the Stokes equation. We show the well-posedness of the new EG approach and prove that the scheme converges optimally. For the solution of the resulting large-scale indefinite linear systems we propose robust block preconditioners, yielding scalable results independent of the discretization and physical parameters. Numerical results confirm the convergence rates of the discretization and also the robustness of the linear solvers for a variety of test problems.
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