A stabilized finite element method for the Stokes problem based on polynomial pressure projections
A stabilized finite element method for the Stokes problem based on polynomial pressure projections
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DOI：
10.1002/fld.752
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发表时间：
2004-09-20
影响因子：
1.8
通讯作者：
Bochev, PB
中科院分区：
文献类型：
--
作者：
Dohrmann, CR;Bochev, PB
提出了求解斯托克斯问题的一种新的稳定化有限元方法。该方法是通过修改的混合变分方程，通过使用局部L2多项式压力投影。我们的稳定化方法的动机是固有的不一致性的等阶近似的斯托克斯方程，这导致了不稳定的混合有限元方法。与最小化的压力-速度不匹配的压力投影结合的应用消除了这种不一致性，并导致一个稳定的变分formulation. Different稳定方法，本方法不需要指定的稳定参数或高阶导数的计算，总是导致一个对称的线性系统。新方法可以在单元级实现，对于单纯网格上的仿射有限元族，它可以简化为对弱连续性方程的简单修改。数值结果提出了各种等阶连续的速度和压力元素在二维和三维。版权所有（C）2004约翰威利父子有限公司。
A new stabilized finite element method for the Stokes problem is presented. The method is obtained by modification of the mixed variational equation by using local L 2 polynomial pressure projections. Our stabilization approach is motivated by the inherent inconsistency of equal-order approximations for the Stokes equations, which leads to an unstable mixed finite element method. Application of pressure projections in conjunction with minimization of the pressure-velocity mismatch eliminates this inconsistency and leads to a stable variational formulation.Unlike other stabilization methods, the present approach does not require specification of a stabilization parameter or calculation of higher-order derivatives, and always leads to a symmetric linear system. The new method can be implemented at the element level and for affine families of finite elements on simplicial grids it reduces to a simple modification of the weak continuity equation. Numerical results are presented for a variety of equal-order continuous velocity and pressure elements in two and three dimensions. Copyright (C) 2004 John Wiley Sons, Ltd.