Convergence analysis of dynamically regularized Lagrange multiplier pressure correction method for the incompressible Navier-Stokes equations
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| Format: | Preprint |
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2026
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| _version_ | 1866917348836900864 |
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| author | Shen, Yi Lan, Rihui Wang, Hua |
| author_facet | Shen, Yi Lan, Rihui Wang, Hua |
| contents | We propose first-order pressure-correction scheme for the incompressible Navier-Stokes equations, incorporating the recently developed the Dynamically Regularized Lagrange Multiplier (DRLM) methods. The resulting algorithms are fully decoupled and require solving only Poisson-type equations at each time step. Moreover, it exhibits unconditional energy stability. This paper provides a rigorous error analysis for the first-order scheme, establishing optimal error estimates for both velocity and pressure. Specifically, we employ mathematical induction to derive sharp velocity error bounds, while leveraging the inf-sup condition to prove optimal convergence rate for the pressure. To validate our theoretical findings, we present two numerical experiments demonstrating the accuracy and robustness of the method. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_16032 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Convergence analysis of dynamically regularized Lagrange multiplier pressure correction method for the incompressible Navier-Stokes equations Shen, Yi Lan, Rihui Wang, Hua Numerical Analysis We propose first-order pressure-correction scheme for the incompressible Navier-Stokes equations, incorporating the recently developed the Dynamically Regularized Lagrange Multiplier (DRLM) methods. The resulting algorithms are fully decoupled and require solving only Poisson-type equations at each time step. Moreover, it exhibits unconditional energy stability. This paper provides a rigorous error analysis for the first-order scheme, establishing optimal error estimates for both velocity and pressure. Specifically, we employ mathematical induction to derive sharp velocity error bounds, while leveraging the inf-sup condition to prove optimal convergence rate for the pressure. To validate our theoretical findings, we present two numerical experiments demonstrating the accuracy and robustness of the method. |
| title | Convergence analysis of dynamically regularized Lagrange multiplier pressure correction method for the incompressible Navier-Stokes equations |
| topic | Numerical Analysis |
| url | https://arxiv.org/abs/2603.16032 |