Analysis of a Hybridized/Interface Stabilized Finite Element Method for the Stokes Equations
Analysis of a Hybridized/Interface Stabilized Finite Element Method for the Stokes Equations
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斯托克斯方程的混合/界面稳定有限元法分析
DOI：
10.1137/16m1083839
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发表时间：
2016
期刊：
影响因子：
--
通讯作者：
G. N. Wells
中科院分区：
文献类型：
--
作者：
S. Rhebergen;G. N. Wells
研究了求解Stokes方程的杂交间断Galerkin有限元方法的稳定性和误差分析。该方法是局部保守的，并为特定的空间选择的速度场是逐点螺线管。证明了该方法对等阶和局部Taylor-Hood型空间都是inf-sup稳定的，并给出了先验误差估计。所考虑的方法可以被构造为具有相同的全局代数结构作为一个符合Galerkin方法，不像标准的不连续Galerkin方法，有更多的自由度比符合Galerkin方法在一个给定的网格。我们断言，这种方法是其中最简单和最灵活的有限元方法的斯托克斯流，提供当地的质量守恒。有了这个贡献的数学基础的建立，这支持的性能的方法，已被观察到的实验在其他作品。
Stability and error analysis of a hybridized discontinuous Galerkin finite element method for Stokes equations is presented. The method is locally conservative, and for particular choices of spaces the velocity field is point-wise solenoidal. It is shown that the method is inf-sup stable for both equal-order and locally Taylor--Hood-type spaces, and a priori error estimates are developed. The considered method can be constructed to have the same global algebraic structure as a conforming Galerkin method, unlike standard discontinuous Galerkin methods that have a greater number of degrees of freedom than conforming Galerkin methods on a given mesh. We assert that this method is among the simplest and most flexible finite element approaches for Stokes flow that provide local mass conservation. With this contribution the mathematical basis is established, and this supports the performance of the method that has been observed experimentally in other works.