Convergence analysis of the dynamically regularized Lagrange multiplier method for the incompressible Navier-Stokes equations
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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866915451762638848 |
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| author | Doan, Cao-Kha Hoang, Thi-Thao-Phuong Ju, Lili Lan, Rihui |
| author_facet | Doan, Cao-Kha Hoang, Thi-Thao-Phuong Ju, Lili Lan, Rihui |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2508_14007 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Convergence analysis of the dynamically regularized Lagrange multiplier method for the incompressible Navier-Stokes equations Doan, Cao-Kha Hoang, Thi-Thao-Phuong Ju, Lili Lan, Rihui Numerical Analysis 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. |
| title | Convergence analysis of the dynamically regularized Lagrange multiplier method for the incompressible Navier-Stokes equations |
| topic | Numerical Analysis |
| url | https://arxiv.org/abs/2508.14007 |