Stress Estimation in Viscous Flows Using an Iterative Tikhonov Regularized Stokes Inverse Model
Abstract
:1. Introduction
2. Stokes Inverse Model (SIM) Formulation
3. Existence, Uniqueness and Error Estimation
3.1. Existence and Uniqueness of the Solution for the Stokes Inverse Problem
3.2. Convergence Analysis for the Stokes Inverse Model
3.3. Error Estimation for the Perturbed Data
4. Numerical Approach
4.1. Variational Formulation
4.2. Finite Element Approximation
5. Stoke Inverse Model Validation
5.1. Velocity Construction
5.2. Determination of the Regularization Parameter
5.3. Model Validation Results
5.4. Model Validation for Perturbed Velocities
6. Conclusions
Author Contributions
Funding
Data Availability Statement
Conflicts of Interest
References
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Characteristic Variables | Description | Primary Units |
---|---|---|
L | Characteristic length | |
U | Characteristic velocity | |
Characteristic force | ||
Characteristic pressure | ||
Characteristic regularization parameter |
Noise Level | Proper | Iterations | Stress Error | Numerical Velocity Error | Reconstructed Velocity Error |
---|---|---|---|---|---|
7 | |||||
12 |
Noise Level | Proper | Iterations | Stress Error | Numerical Velocity Error | Reconstructed Velocity Error |
---|---|---|---|---|---|
104 | |||||
111 |
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Gao, Y.; Wang, Y.; Zhang, J. Stress Estimation in Viscous Flows Using an Iterative Tikhonov Regularized Stokes Inverse Model. Mathematics 2025, 13, 1884. https://doi.org/10.3390/math13111884
Gao Y, Wang Y, Zhang J. Stress Estimation in Viscous Flows Using an Iterative Tikhonov Regularized Stokes Inverse Model. Mathematics. 2025; 13(11):1884. https://doi.org/10.3390/math13111884
Chicago/Turabian StyleGao, Yuanhao, Yang Wang, and Jizhou Zhang. 2025. "Stress Estimation in Viscous Flows Using an Iterative Tikhonov Regularized Stokes Inverse Model" Mathematics 13, no. 11: 1884. https://doi.org/10.3390/math13111884
APA StyleGao, Y., Wang, Y., & Zhang, J. (2025). Stress Estimation in Viscous Flows Using an Iterative Tikhonov Regularized Stokes Inverse Model. Mathematics, 13(11), 1884. https://doi.org/10.3390/math13111884