Error analysis of fully discrete mixed finite element data assimilation schemes for the Navier-Stokes equations
Error analysis of fully discrete mixed finite element data assimilation schemes for the Navier-Stokes equations
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纳维-斯托克斯方程全离散混合有限元数据同化方案的误差分析
DOI：
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发表时间：
2019
影响因子：
1.7
通讯作者：
J. Novo
中科院分区：
文献类型：
--
作者：
Bosco Garc'ia;J. Novo
在这篇文章中，我们考虑了在空间上用inf-sup稳定混合有限元方法来逼近N-S方程的全离散逼近。分析了一种连续降尺度数据同化算法，该算法用不同类型的内插算子表示粗尺度上的测量值。对于时间离散，考虑了隐式欧拉格式、隐式和半隐式二阶后向微分公式。对于完全离散近似和对应于测量的参考解之间的误差，所有方法都得到了时间一致的误差估计。对于空间离散，我们同时考虑了Galerkin方法和Grad-div稳定的Galerkin方法。对于最后一种格式，得到了常数不依赖于粘性的反幂的误差界。
In this paper we consider fully discrete approximations with inf-sup stable mixed finite element methods in space to approximate the Navier-Stokes equations. A continuous downscaling data assimilation algorithm is analyzed in which measurements on a coarse scale are given represented by different types of interpolation operators. For the time discretization an implicit Euler scheme, an implicit and a semi-implicit second-order backward differentiation formula are considered. Uniform-in-time error estimates are obtained for all the methods for the error between the fully discrete approximation and the reference solution corresponding to the measurements. For the spatial discretization we consider both the Galerkin method and the Galerkin method with grad-div stabilization. For the last scheme error bounds in which the constants do not depend on inverse powers of the viscosity are obtained.
影响因子：
3.9
作者：
D. Arndt;Helene Dallmann;G. Lube
通讯作者：
D. Arndt;Helene Dallmann;G. Lube
影响因子：
2.1
作者：
Helene Dallmann;D. Arndt;G. Lube
通讯作者：
Helene Dallmann;D. Arndt;G. Lube
DOI：
10.1016/j.cma.2018.09.004
发表时间：
2018-05
影响因子：
7.2
作者：
Adam Larios;L. Rebholz;C. Zerfas
通讯作者：
Adam Larios;L. Rebholz;C. Zerfas