Convergence Analysis of Dynamically Regularized Lagrange Multiplier Pressure Correction Method for the Incompressible Navier–Stokes Equations

ABSTRACT We propose a first‐order pressure‐correction scheme for the incompressible Navier‐Stokes equations, incorporating the recently developed Dynamically Regularized Lagrange Multiplier (DRLM) methods. The resulting algorithm is 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.