论文标题
OSEEN方程的广义弱甘油素法
A Generalized Weak Galerkin method for Oseen equation
论文作者
论文摘要
在这项工作中，作者为时间依赖性OSEEN方程引入了广义弱彩手（GWG）有限元方法。广义的弱Galerkin方法基于一个新框架，用于近似梯度运算符。制定和分析了半二淀粉和完全差异的数值方案，并分析其收敛性，稳定性和误差估计。开发了广义{\ em {inf-sup}}条件以帮助收敛分析。向后的Euler离散化用于全差异方案的设计。最佳顺序的错误估计是数学上建立的，并通过一些基准示例进行数值验证。
In this work, the authors introduce a generalized weak Galerkin (gWG) finite element method for the time-dependent Oseen equation. The generalized weak Galerkin method is based on a new framework for approximating the gradient operator. Both a semi-discrete and a fully-discrete numerical scheme are developed and analyzed for their convergence, stability, and error estimates. A generalized {\em{inf-sup}} condition is developed to assist the convergence analysis. The backward Euler discretization is employed in the design of the fully-discrete scheme. Error estimates of optimal order are established mathematically, and they are validated numerically with some benchmark examples.
