Quasi-optimality of a pressure-robust nonconforming finite element method for the Stokes-Problem
Quasi-optimality of a pressure-robust nonconforming finite element method for the Stokes-Problem
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DOI：
10.1090/mcom/3344
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发表时间：
2017-02
期刊：
影响因子：
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通讯作者：
A. Linke;C. Merdon;M. Neilan;Felix Neumann
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文献类型：
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作者：
A. Linke;C. Merdon;M. Neilan;Felix Neumann
几乎所有经典的求解不可压Stokes方程的下超稳定混合有限元方法都不具有压力鲁棒性，即速度误差与压力有关。然而，最近的研究结果表明，压力鲁棒性可以恢复的非标准离散化的右手边。这种变分犯罪引入了一致性错误的方法，可以估计在一个简单的方式提供的精确的速度解是足够光滑的。本文的目的是分析具有低正则性的压力鲁棒格式。数值分析采用无发散协调Stokes有限元方法作为理论工具。作为一个例子，压力鲁棒的速度和压力的先验误差估计将提出（一阶）的Crock-Crouzeix-Raviart元素。分析中的一个关键特征是误差依赖于右侧数据的亥姆霍兹投影仪，而不是整个数据项。数值例子说明了理论结果。引用
Nearly all classical inf-sup stable mixed finite element methods for the incompressible Stokes equations are not pressure-robust, ie, the velocity error is dependent on the pressure. However, recent results show that pressure-robustness can be recovered by a nonstandard discretization of the right-hand side alone. This variational crime introduces a consistency error in the method which can be estimated in a straightforward manner provided that the exact velocity solution is sufficiently smooth. The purpose of this paper is to analyze the pressure-robust scheme with low regularity. The numerical analysis applies divergence-free-conforming Stokes finite element methods as a theoretical tool. As an example, pressure-robust velocity and pressure a priori error estimates will be presented for the (first-order) nonconforming Crouzeix–Raviart element. A key feature in the analysis is the dependence of the errors on the Helmholtz projector of the right-hand side data, and not on the entire data term. Numerical examples illustrate the theoretical results. References