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<p>This work deals with the finite element approximation of the non-stationary Navier–Stokes equations with a friction-type leak interface condition. We propose a fully discrete finite element scheme. The discrete variational inequality can be expressed equally as a Lagrange multiplier formulation. We demonstrate the stability and well-posedness of the discrete scheme and derive the error estimates. Additionally, we introduce the Uzawa algorithms and examine its convergence.Numerical examples are presented to confirm the theoretical results.</p>

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The Finite Element Method for the Navier–Stokes Equation with a Frictional Interface Condition

  • 期刊论文

  • 发表日期：

    2025年5月21日

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  • Rui Luo,
  • Ping Zeng,
  • Guanyu Zhou

摘要

This work deals with the finite element approximation of the non-stationary Navier–Stokes equations with a friction-type leak interface condition. We propose a fully discrete finite element scheme. The discrete variational inequality can be expressed equally as a Lagrange multiplier formulation. We demonstrate the stability and well-posedness of the discrete scheme and derive the error estimates. Additionally, we introduce the Uzawa algorithms and examine its convergence.Numerical examples are presented to confirm the theoretical results.