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{\large 
\\ Lijian Jiang \\
{\bf Operator Splitting Methods in 4D Variational Data Assimilation. 
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Department of Mathematics \\
Texas A & M University \\ 
College Station, TX 77843-3368 \\
{\tt ljjiang@math.tamu.edu}\\
Craig C. Douglas \\ %% Departments of Computer Science and Mechanical Engineering, University of Kentucky, Lexington, KY 40506-0046; Department of Computer Science, Yale University, New Haven, CT. email: craig.douglas@uky.edu
Yalchin Efendiev %% Department of Mathematics, Texas A & M University, College Station, TX 77843-3368. email: efendiev@math.tamu.edu
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In this paper, we give a framework 4D variational data assimilation (4D-Var) in Hilbert Spaces. In functional partial diﬀerential equation setting, the adjoint equation method and Marchuk-Strang operator splitting are discussed. Convergence analysis of the operator splitting method is investigated for the functional 4D-Var. 
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