Global in time stability and accuracy of IMEX-FEM data assimilation schemes for Navier–Stokes equations
Global in time stability and accuracy of IMEX-FEM data assimilation schemes for Navier–Stokes equations
复制标题
DOI：
10.1016/j.cma.2018.09.004
复制
发表时间：
2018-05
影响因子：
7.2
通讯作者：
Adam Larios;L. Rebholz;C. Zerfas
中科院分区：
文献类型：
--
作者：
Adam Larios;L. Rebholz;C. Zerfas
我们研究了不可压缩Navier-Stokes方程的数值格式，使用IMEX时间离散化、有限元空间离散化，并配备了连续数据同化（Azouani等人（2014）最近开发的一种技术）。我们分析了所提方法的稳定性和精度，并在时间步长和数据同化参数的限制下证明了该方法的适定性、长时间稳定性和长时间精度估计。我们给出了几个数值试验的结果来说明该理论，并表明，为了获得良好的结果，离散化参数的选择和单元的选择是至关重要的。
We study numerical schemes for incompressible Navier–Stokes equations using IMEX temporal discretizations, finite element spatial discretizations, and equipped with continuous data assimilation (a technique recently developed by Azouani et al. (2014)). We analyze stability and accuracy of the proposed methods, and are able to prove well-posedness, long time stability, and long time accuracy estimates, under restrictions of the time step size and data assimilation parameter. We give results for several numerical tests that illustrate the theory, and show that, for good results, the choice of discretization parameter and element choices can be critical.