Research

Main contributions:

1. the first convergence and optimality results of adaptive FEMs for the Hodge-Laplacian [L.(2019)SINUM, L.(2021)MathComp];

2. novel entropy-based analysis of greedy algorithms (reduced basis method, EIM, OGA) [L.&Siegel(2024)M3AS, L.(2025)SINUM];

3. interplay between preconditioning and a posteriori error estimation [L.&Zikatanov(2021)CAMWA, (2025)MathComp];

4. the first discontinuous Galerkin method for the Hodge-Laplace equation [Hong&L.&Xu(2022)MathComp];

5. provably optimal solvers for computing harmonic vector fields [L.(2024)FoCM];

6. the first energy-preserving exponential integrator [L.&Wu(2016)SISC].

Papers on arXiv

My Google Scholar

Papers on MathSciNet

Selected papers

1. "Some p-robust a posteriori error estimates based on auxiliary spaces", arXiv:2511.06603

2. "Smoother-type a posteriori error estimates for finite element methods" with Han Shui, arXiv:2510.07677

3. "Some super-approximation rates of ReLU neural networks for Korobov functions" with Guozhi Zhang, arXiv:2507.10345

4. "Nodal auxiliary a posteriori error estimates" with Ludmil Zikatanov, Math. Comp., arXiv:2010.06774, DOI: 10.1090/mcom/4141 

5. "A new rational approximation algorithm via the empirical interpolation method" with Aidi Li, SISC,  (47)5, (2025) A2559-A2582.

6. "Reduced Krylov basis methods for parametric partial differential equations" with Cheng Zuo, Ludmil Zikatanov, SINUM, 63(2), (2025) 976-999.

7. "A new analysis of empirical interpolation methods and Chebyshev greedy algorithms", SINUM, 63(2), (2025) 931-948.

8. "A reduced conjugate gradient basis method for fractional diffusion" with Cheng Zuo, Ludmil Zikatanov, SISC, S68-S87 (2024)

9. "Entropy-based convergence rates for greedy algorithms" with Jonathan Siegel, M3AS, 34(5), (2024) 779-802.

10. "Nodal auxiliary space preconditioning for the surface de Rham complex", Found. Comput. Math., 24 (2024) 1019-1048.

11. "An extended Galerkin analysis in finite element exterior calculus" with Qingguo Hong, Jinchao Xu, Math. Comp., Vol. 91 (2022) 1077-1106.

12. "New stabilized P1P0 finite element methods for nearly inviscid and incompressible flows" with Ludmil Zikatanov, CMAME, 393 (2022) 141815.

13. "Residual-based a posteriori error estimates of mixed methods for a three-field Biot's consolidation model" with L. Zikatanov, IMA J. Numer. Anal., 42 (2022) 620-648.

14. "A posteriori error estimates of finite element methods by preconditioning" with L. Zikatanov, CAMWA, 91 (2021) 192-201.

15. "Quasi-optimal adaptive mixed finite element methods for controlling natural norm errors", Math. Comp., 90 (2021) 565-593.

16. "A unified framework of continuous and discontinuous Galerkin methods for solving the incompressible Navier-Stokes equation" with Xi Chen et al., JCP, 422 (2020) 109799.

17. "Superconvergent recovery of Raviart–Thomas mixed finite elements on triangular grids" with Randolph Bank, J. Sci. Comput., 57 (2019) 1882-1905.

18. "Some convergence and optimality results of adaptive mixed methods in finite element exterior calculus", SINUM, 57 (2019) 2019-2042.

19. "Global superconvergence of the lowest-order mixed finite element on mildly structured meshes", SINUM, 56 (2018) 792-815.

20. "Functionally fitted energy-preserving methods for solving nonlinear oscillatory Hamiltonian systems" with Xinyuan Wu, SINUM, 54 (2016) 2036-2059.

21. "Exponential integrators preserving first integrals or Lyapunov functions for conservative or dissipative systems" with Xinyuan Wu, SISC, 38 (2016) A1876-A1885.

22. "General local energy-preserving integrators for solving multi-symplectic Hamiltonian PDEs" with Xinyuan Wu, JCP, 301 (2015) 141-166.

Collaborators: James Adler, Randolph Bank, Xi Chen, Michael Holst, Xiaozhe Hu, Qingguo Hong, Aidi Li, Zhengqi Liu, Han Shui, Jonathan Siegel, Yupeng Wang, Xinyuan Wu, Jinchao Xu, Guozhi Zhang, Ludmil Zikatanov, Cheng Zuo