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April 1, 2026Numerical Methods for Partial Differential Equations1 citations

Modified Fictitious Domain Method for Unsteady Navier-Stokes Equations

A Modified Brinkman Penalization Fictitious Domain Method for the Unsteady Navier‐Stokes Equations

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Authors

ZBZhanybek BaitulenovMOMaxim A. OlshanskiiATA. Temirbekov

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Overview

This method improves convergence in solving unsteady Navier-Stokes equations, enhancing fluid motion modeling.

Key Points

  • The research aims to modify the fictitious domain method for better solutions to the unsteady Navier-Stokes equations for fluid motion.
  • Modified the fictitious domain method with solution-dependent parameter selection.
  • Established global and local existence and convergence of solutions.
  • Applied a pointwise divergence-free finite element method for discretization.
  • Proved existence and convergence for weak and strong solutions.
  • Achieved a new higher-order convergence rate for the penalization parameter.
  • Illustrated method performance with a numerical example.
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Cite This Study

Baitulenov et al. (2026) studied this question.

synapsesocial.com/papers/69cd7b155652765b073a8be5https://doi.org/10.1002/num.70089
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