Genming Bai

Research Interests

• Numerical methods and analysis for linear and nonlinear PDEs
• Computational science

Employment

Education

Awards

Publications

1. G. Bai. A spherical harmonic pseudo-spectral approach to mean curvature flow of surfaces with spherical topology. Submitted. arXiv:2606.21615

2. G. Bai and S. Veerapaneni. A structure-preserving fast spectral method for locally inextensible vesicles with tangential smoothing. To be submitted.

3. G. Bai, H. Garcke, and S. Veerapaneni. A convergent finite element method for two-phase Stokes flow driven by surface tension. Foundations of Computational Mathematics, to appear. arXiv:2509.20111

4. G. Bai, H. Garcke, and S. Veerapaneni. Convergence analysis for the Barrett–Garcke–Nürnberg method of transport type. Numerische Mathematik, 2025. doi: 10.1007/s00211-025-01521-3

5. G. Bai, J. Cui, and B. Li. Discrete stochastic maximal L^p-L^q regularity of semi-discrete finite element methods. Submitted.

6. G. Bai, B. Li, and Y. Xie. Convergence of BGN-type method for surface diffusion. To be submitted.

7. G. Bai, B. Kovács, and B. Li. Maximal regularity of parametric finite element method for parabolic equations on evolving surfaces. IMA Journal of Numerical Analysis, 2025. doi: 10.1093/imanum/draf082

8. G. Bai, D. Leykekhman, and B. Li. Weak maximum principle of finite element methods for parabolic equations in polygonal domains. Numerische Mathematik, 2025. doi: 10.1007/s00211-025-01453-y

9. G. Bai, X. Gui, and B. Li. Convergence of multistep projection methods for harmonic map heat flows into general surfaces. Numerische Mathematik, 2025. doi: 10.1007/s00211-025-01464-9

10. G. Bai and B. Li. Convergence of parametric finite element methods of the Barrett–Garcke–Nürnberg type for curve shortening flow. Mathematics of Computation, 2024 (70 pages). doi: 10.1090/mcom/4019

11. G. Bai, J. Hu, and B. Li. A convergent evolving finite element method with artificial tangential motion for surface evolution under a prescribed velocity field. SIAM Journal on Numerical Analysis, 2024. doi: 10.1137/23M156968X

12. G. Bai, J. Hu, and B. Li. Arbitrary high-order mass and energy conserving methods for the Schrödinger equation. SIAM Journal on Scientific Computing, 2024. doi: 10.1137/22M152178X

13. G. Bai and B. Li. A new approach to the analysis of parametric finite element approximation to mean curvature flow. Foundations of Computational Mathematics, 2023 (65 pages). doi: 10.1007/s10208-023-09622-x

14. G. Bai and B. Li. Erratum: Convergence of Dziuk’s semidiscrete finite element method for mean curvature flow of closed surfaces with high-order finite elements. SIAM Journal on Numerical Analysis, 2023. doi: 10.1137/22M1521791

15. G. Bai, B. Li, and Y. Wu. A constructive low-regularity integrator for the one-dimensional cubic nonlinear Schrödinger equation under Neumann boundary condition. IMA Journal of Numerical Analysis, 2022. doi: 10.1093/imanum/drac075

16. G. Bai, U. Koley, S. Mishra, and R. Molinaro. Physics informed neural networks (PINNs) for approximating nonlinear dispersive PDEs. Journal of Computational Mathematics, 2021. doi: 10.4208/jcm.2101-m2020-0342

Links

• Foundations of Computational Mathematics
• Numerische Mathematik
• Mathematics of Computation
• IMA Journal of Numerical Analysis
• SIAM Journal on Numerical Analysis