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arXiv · 2508.14007

Convergence analysis of the dynamically regularized Lagrange multiplier method for the incompressible Navier-Stokes equations

Cao-Kha Doan·Thi-Thao-Phuong Hoang·Lili Ju·Rihui Lan
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Abstract

This paper is concerned with temporal convergence analysis of the recently introduced Dynamically Regularized Lagrange Multiplier (DRLM) method for the incompressible Navier-Stokes equations. A key feature of the DRLM approach is the incorporation of the kinetic energy evolution through a quadratic dynamic equation involving a time-dependent Lagrange multiplier and a regularization parameter. We apply the backward Euler method with an explicit treatment of the nonlinear convection term and show the unique solvability of the resulting first-order DRLM scheme. Optimal error estimates for the velocity and pressure are established based on a uniform bound on the Lagrange multiplier and mathematical induction. Numerical results confirm the theoretical convergence rates and error bounds that decay with respect to the regularization parameter.

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Cao-Kha Doan, Thi-Thao-Phuong Hoang, Lili Ju, Rihui Lan. 2025-08-19. Convergence analysis of the dynamically regularized Lagrange multiplier method for the incompressible Navier-Stokes equations. https://arxiv.org/abs/2508.14007

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