论文标题
基于涡度的速度触发特征值问题的错误估计值
Error estimates for a vorticity-based velocity-stress formulation of the Stokes eigenvalue problem
论文作者
论文摘要
本文的目的是分析二维Stokes特征值问题的混合配方，其中未知数是应力和速度，而可以通过简单的应力后孔来恢复压力。应力张量是根据流体的涡度编写的，从而导致一种融合了这种物理特征的替代混合配方。我们提出了一种混合数值方法，其中应力与合适的nédelec有限元近似，而速度则以$ k \ geq 0 $的分段多项式近似。借助紧凑的操作者理论，我们得出了方法和光谱正确性的收敛性。此外，我们为我们的光谱问题提出了可靠有效的后验误差估计器。我们报告了不同域中的数值测试，计算频谱和收敛顺序，以及针对拟议估计器的计算分析。此外，我们使用相应的误差估计器来驱动自适应方案，并报告数值测试的结果，使我们能够评估这种方法的性能。
The aim of this paper is to analyze a mixed formulation for the two dimensional Stokes eigenvalue problem where the unknowns are the stress and the velocity, whereas the pressure can be recovered with a simple postprocess of the stress. The stress tensor is written in terms of the vorticity of the fluid, leading to an alternative mixed formulation that incorporates this physical feature. We propose a mixed numerical method where the stress is approximated with suitable Nédelec finite elements, whereas the velocity is approximated with piecewise polynomials of degree $k\geq 0$. With the aid of the compact operators theory we derive convergence of the method and spectral correctness. Moreover, we propose a reliable and efficient a posteriori error estimator for our spectral problem. We report numerical tests in different domains, computing the spectrum and convergence orders, together with a computational analysis for the proposed estimator. In addition, we use the corresponding error estimator to drive an adaptive scheme, and we report the results of a numerical test, that allow us to assess the performance of this approach.
