Stabilized Galerkin finite element methods for convection dominated and incompressible flow problems
Stabilized Galerkin finite element methods for convection dominated and incompressible flow problems
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针对对流主导和不可压缩流动问题的稳定伽辽金有限元方法
DOI：
10.4064/-29-1-85-104
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发表时间：
1994
期刊：
影响因子：
--
通讯作者：
G. Lube
中科院分区：
文献类型：
--
作者：
G. Lube
本文分析了一类稳定化的有限元列式，它们分别用于（i）二阶椭圆边值问题（扩散-对流-反应模型）和（ii）Navier-Stokes问题（不可压缩流模型）的计算。这些稳定化技术防止了可能由（i）、（ii）中的主要对流/反应项或（ii）中的速度/压力插值函数的不适当组合产生的数值不稳定性。稳定性和收敛性的非均匀网格的结果，在整个范围内从扩散到对流/反应为主的情况。特别是，我们恢复结果的流线迎风和Galerkin/最小二乘法。给出了低阶插值函数的数值结果。
In this paper, we analyze a class of stabilized finite element formulations used in computation of (i) second order elliptic boundary value problems (diffusion-convection-reaction model) and (ii) the Navier–Stokes problem (incompressible flow model). These stabilization techniques prevent numerical instabilities that might be generated by dominant convection/reaction terms in (i), (ii) or by inappropriate combinations of velocity/pressure interpolation functions in (ii). Stability and convergence results on non-uniform meshes are given in the whole range from diffusion to convection/reaction dominated situations. In particular, we recover results for the streamline upwind and Galerkin/least-squares methods. Numerical results are presented for low order interpolation functions.