Location
Havener Center, Miner Lounge / Wiese Atrium, 1:30pm-3:30pm
Start Date
4-2-2026 1:30 PM
End Date
4-2-2026 3:30 PM
Presentation Date
April 2, 2026; 1:30pm-3:30pm
Description
Variational data assimilation (VDA) determines the initial condition of a dynamical system by minimizing the mismatch between model predictions and observed data. This work studies VDA for the time-dependent Stokes–Darcy system with the BJSJ interface condition. The problem is formulated as a PDE-constrained optimization problem, and the first-order optimality system is derived using the Gâteaux derivative and adjoint variables. A steepest descent method is applied for efficient computation. Spatial and temporal discretizations are carried out using the finite element method and backward Euler scheme, respectively. Numerical results confirm accuracy and convergence.
Biography
I am a third-year PhD student in mathematics, specializing in computational mathematics and scientific computing. My research focuses on variational data assimilation, particularly the development and analysis of finite element methods for coupled fluid flow systems. I work on models such as the Stokes–Darcy and Navier–Stokes–Darcy systems with Beavers–Joseph–Saffman–Jones (BJSJ) interface conditions. My research also involves PDE-constrained optimization, where I employ adjoint-based methods to derive optimality systems and compute gradients efficiently. In addition, I design and analyze gradient-based algorithms, such as the steepest descent method, to ensure stable and efficient numerical performance. My goal is to develop accurate and robust computational methods for complex Multiphysics flow problems.
Meeting Name
2026 - Miners Solving for Tomorrow Research Conference
Department(s)
Mathematics and Statistics
Document Type
Poster
Document Version
Final Version
File Type
event
Language(s)
English
Rights
© 2026 The Authors, All rights reserved
Included in
Variational Data Assimilation with Steepest Descent Method for Coupled Time-Dependent Stokes-Darcy Model with BJSJ Interface Condition
Havener Center, Miner Lounge / Wiese Atrium, 1:30pm-3:30pm
Variational data assimilation (VDA) determines the initial condition of a dynamical system by minimizing the mismatch between model predictions and observed data. This work studies VDA for the time-dependent Stokes–Darcy system with the BJSJ interface condition. The problem is formulated as a PDE-constrained optimization problem, and the first-order optimality system is derived using the Gâteaux derivative and adjoint variables. A steepest descent method is applied for efficient computation. Spatial and temporal discretizations are carried out using the finite element method and backward Euler scheme, respectively. Numerical results confirm accuracy and convergence.
Comments
Advisor: Xiaoming He, hex@mst.edu