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October 11, 2025Mathematics0 citationsOpen Access

Smooth Solutions to 3D Incompressible Navier-Stokes Equations via Finite Element Approximation

On Smooth Solution to Three-Dimensional Incompressible Navier–Stokes Equations Based on Numerical Solutions by Finite Element Approximation

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Authors

FLFengnan LiuJCJun CaoZZZ.L. Zhang

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Overview

Numerical methods establish a unique strong solution for 3D Navier-Stokes equations, suggesting effective convergence techniques.

Key Points

  • Smooth initial data leads to a unique strong solution that remains smooth, ensuring stability of the system.
  • The numerical method employs a second-order backward differentiation formula, demonstrating strong convergence as discretization parameters decrease.
  • Extensive finite element scheme provides a structured approach to solving the three-dimensional incompressible Navier-Stokes equations.
  • Results confirm that bounded discrete solutions converge to the exact solution under defined conditions.

Cite This Study

Liu et al. (2025) studied this question.

synapsesocial.com/papers/68e9b1d0ba7d64b6fc132c38https://doi.org/10.3390/math13193236
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