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首页> 外文期刊>Applied numerical mathematics >Analysis of a stabilized finite element approximation of the Oseen equations using orthogonal subscales
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Analysis of a stabilized finite element approximation of the Oseen equations using orthogonal subscales

机译：使用正交子标度分析Oseen方程的稳定有限元逼近

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摘要

In this paper we present a stabilized finite element formulation to solve the Oseen equations as a model problem involving both convection effects and the incompressibility restriction. The need for stabilization techniques to solve this problem arises because of the restriction in the possible choices for the velocity and pressure spaces dictated by the inf-sup condition, as well as the instabilities encountered when convection is dominant. Both can be overcome by resorting from the standard Galerkin method to a stabilized formulation. The one presented here is based on the subgrid scale concept, in which unresolvable scales of the continuous solution are approximately accounted for. In particular, the approach developed herein is based on the assumption that unresolved subscales are orthogonal to the finite element space. It is shown that this formulation is stable and optimally convergent for an adequate choice of the algorithmic parameters on which the method depends.
机译：在本文中，我们提出了一种稳定的有限元公式来解决Oseen方程，这是一个涉及对流效应和不可压缩性约束的模型问题。对稳定技术来解决该问题的需求的出现是由于对由进气条件决定的速度和压力空间的可能选择的限制，以及在对流占优势时遇到的不稳定性。可以通过采用标准的Galerkin方法克服稳定的配方来克服这两种情况。这里介绍的一个是基于子网格规模的概念，其中连续解决方案的不可解决规模被近似解决。特别地，本文开发的方法基于以下假设：未解决的子尺度与有限元素空间正交。结果表明，对于适当选择该方法所依赖的算法参数，该公式是稳定的并且最佳收敛。

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