A finite element data assimilation method for the wave equation
A finite element data assimilation method for the wave equation
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DOI：
10.1090/mcom/3508
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发表时间：
2018-11
期刊：
影响因子：
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通讯作者：
E. Burman;A. Feizmohammadi;L. Oksanen
中科院分区：
文献类型：
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作者：
E. Burman;A. Feizmohammadi;L. Oksanen
本文设计了一种原始-对偶稳定化有限元方法，用于数值逼近声波方程的数据同化问题。对于正问题，分段仿射，连续，有限元函数用于在空间上的近似和向后微分用于时间。在离散水平上添加稳定化项。这些术语的设计是由数值稳定性和连续问题的稳定性驱动的，其目标是使计算误差最小化。误差估计，然后推导出的数值方案的近似性质和连续问题的稳定性方面是最佳的。离散化（光滑）域边界和数据中的其他扰动的影响包括在分析中。
We design a primal-dual stabilized finite element method for the numerical approximation of a data assimilation problem subject to the acoustic wave equation. For the forward problem, piecewise affine, continuous, finite element functions are used for the approximation in space and backward differentiation is used in time. Stabilizing terms are added on the discrete level. The design of these terms is driven by numerical stability and the stability of the continuous problem, with the objective of minimizing the computational error. Error estimates are then derived that are optimal with respect to the approximation properties of the numerical scheme and the stability properties of the continuous problem. The effects of discretizing the (smooth) domain boundary and other perturbations in data are included in the analysis.