Mesh-Free Interpolant Observables for Continuous Data Assimilation  

作　　者：Animikh Biswas Kenneth R.Brown Vincent R.Martinez 

机构地区：[1]Department of Mathematics & Statistics,University of Maryland-Baltimore County,1000 Hilltop Circle,Baltimore,MD 21250,USA [2]Department of Mathematics,University of California-Davis,One Shields Avenue,Davis,CA 95616,USA [3]Department of Mathematics & Statistics,CUNY Hunter College,695 ParkAve,NewYork,NY10065,USA [4]Department of Mathematics,CUNY Graduate Center,3655th Ave,New York,NY10016,USA

出　　处：《Annals of Applied Mathematics》2022年第3期296-355,共60页应用数学年刊（英文版）

基　　金：partially supported by the award PSC-CUNY64335-0052,jointly funded by The Professional Staff Congress and The City University of New York。

摘　　要：This paper is dedicated to the expansion of the framework of general interpolant observables introduced by Azouani,Olson,and Titi for continuous data assimilation of nonlinear partial differential equations.The main feature of this expanded framework is its mesh-free aspect,which allows the observational data itself to dictate the subdivision of the domain via partition of unity in the spirit of the so-called Partition of Unity Method by Babuska and Melenk.As an application of this framework,we consider a nudging-based scheme for data assimilation applied to the context of the two-dimensional Navier-Stokes equations as a paradigmatic example and establish convergence to the reference solution in all higher-order Sobolev topologies in a periodic,mean-free setting.The convergence analysis also makes use of absorbing ball bounds in higherorder Sobolev norms,for which explicit bounds appear to be available in the literature only up to H^(2);such bounds are additionally proved for all integer levels of Sobolev regularity above H^(2).

关 键 词：Continuous data assimilation nudging 2D Navier-Stokes equations general interpolant observables synchronization higher-order convergence partition of unity MESH-FREE Azounai-Olson-Titi algorithm 

分 类 号：O175.29[理学—数学]