@Article{CiCP-29-1273,
author = {Larios , Adam and Victor , Collin},
title = {Continuous Data Assimilation with a Moving Cluster of Data Points for a Reaction Diffusion Equation: A Computational Study},
journal = {Communications in Computational Physics},
year = {2021},
volume = {29},
number = {4},
pages = {1273--1298},
abstract = {<p style="text-align: justify;">Data assimilation is a technique for increasing the accuracy of simulations
of solutions to partial differential equations by incorporating observable data into the
solution as time evolves. Recently, a promising new algorithm for data assimilation
based on feedback-control at the PDE level has been proposed in the pioneering work
of Azouani, Olson, and Titi (2014). The standard version of this algorithm is based on
measurement from data points that are fixed in space. In this work, we consider the
scenario in which the data collection points move in space over time. We demonstrate
computationally that, at least in the setting of the 1D Allen-Cahn reaction diffusion
equation, the algorithm converges with significantly fewer measurement points, up to
an order or magnitude in some cases. We also provide an application of the algorithm
to the estimation of a physical length scale in the case of a uniform static grid.</p>},
issn = {1991-7120},
doi = {https://doi.org/10.4208/cicp.OA-2018-0315},
url = {http://global-sci.org/intro/article_detail/cicp/18652.html}
}