In this talk, I will present efficient numerical schemes based on the Lagrange multiplier approach for the Navier-Stokes equations. By introducing a dynamic equation (involving the kinetic energy, the Lagrange multiplier, and a regularization parameter), we form a new system that incorporates the energy evolution process while remaining equivalent to the original equations. Such nonlinear system is then discretized in time using backward differentiation formulas, resulting in a dynamically regularized Lagrange multiplier (DRLM) method. First- and second-order DRLM schemes are derived and shown to be unconditionally energy stable with respect to the original variables. Optimal error estimates for the velocity and pressure of the first-order DRLM scheme are established through a uniform bound on the Lagrange multiplier and mathematical induction. Numerical experiments demonstrate the accuracy, stability, and robustness of the proposed schemes.
About the Speaker 
I am a Postdoctoral Research Associate in the Department of Mathematical Sciences at Rensselaer Polytechnic Institute, working with Prof. Fengyan Li. I received my Ph.D. in Mathematics from Auburn University in Summer 2026. My research focuses on numerical analysis and scientific computing, including structure-preserving time-stepping methods for evolution PDEs, as well as reduced order models for kinetic equations.
