VARIATIONAL DATA ASSIMILATION and its DECOUPLED ITERATIVE NUMERICAL ALGORITHMS for STOKES-DARCY MODEL

Abstract

In This Paper We Develop and Analyze a Variational Data Assimilation Method with Efficient Decoupled Iterative Numerical Algorithms for the Stokes-Darcy Equations with the Beavers-Joseph Interface Condition. by using Tikhonov Regularization and Formulating the Variational Data Assimilation into an Optimization Problem, We Establish the Existence, Uniqueness, and Stability of the Optimal Solution. based on the Weak Formulation of the Stokes-Darcy Equations, the Lagrange Multiplier Rule is Utilized to Derive the First Order Optimality System for Both the Continuous and Discrete Variational Data Assimilation Problems, Where the Discrete Data Assimilation is based on a Finite Element Discretization in Space and the Backward Euler Scheme in Time. by Rescaling the Optimality System and Then Analyzing its Corresponding Bilinear Forms, We Prove the Optimal Finite Element Convergence Rate with Special Attention Paid to Recovering Uncertainties Missed in the Optimality System. to Solve the Discrete Optimality System Efficiently, Three Decoupled Iterative Algorithms Are Proposed to Address the Computational Cost for Both Well-Conditioned and Ill-Conditioned Variational Data Assimilation Problems, Respectively. Finally, Numerical Results Are Provided to Validate the Proposed Methods.

Department(s)

Mathematics and Statistics

Comments

National Science Foundation, Grant DMS-1722647

International Standard Serial Number (ISSN)

1095-7197; 1064-8275

Document Type

Article - Journal

Document Version

Final Version

File Type

text

Language(s)

English

Rights

© 2024 Society for Industrial and Applied Mathematics, All rights reserved.

Publication Date

01 Apr 2024

Link to Full Text

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