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arXiv · 2512.19580

A modified Brinkman penalization fictitious domain method for the unsteady Navier-Stokes equations

Zhanybek Baitulenov·Maxim Olshanskii·Almas Temirbekov·Nurlan Temirbekov·Syrym Kasenov
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Abstract

This paper investigates a modification of the fictitious domain method with continuation in the lower-order coefficients for the unsteady Navier-Stokes equations governing the motion of an incompressible homogeneous fluid in a bounded 2D or 3D domain. The modification enables {a solution-dependent} choice of the critical parameter. Global-in-time existence and convergence of a weak solution to the auxiliary problem are proved, and local-in-time existence and convergence of a unique strong solution are established. For the strong solution, a new higher-order convergence rate estimate in the penalization parameter is obtained. The introduced framework allows us to apply a pointwise divergence free finite element method as a discretization technique, leading to strongly mass conservative discrete fictitious domain method. A numerical example illustrates the performance of the method.

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Zhanybek Baitulenov, Maxim Olshanskii, Almas Temirbekov, Nurlan Temirbekov, Syrym Kasenov. 2025-12-22. A modified Brinkman penalization fictitious domain method for the unsteady Navier-Stokes equations. https://arxiv.org/abs/2512.19580

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