My research areas include:
1. Finite Element Methods, including Adaptive FEMs, Iterative Solvers, Finite Element Exterior Calculus, Superconvergence, discontinuous Galerkin;
2. Structure-Preserving Methods, such as Energy-Preserving Methods for dynamical systems and Finite Element Exterior Calculus;
3. Adaptive Algorithm for more general problems, such as Reduced Basis Methods, Learning Algorithms, Rational and Neural Network Approximation.
Papers on arXiv
Papers on MathSciNet
Recent papers
"Some p-robust a posteriori error estimates based on auxiliary spaces", arXiv:2511.06603
"Smoother-type a posteriori error estimates for finite element methods", arXiv:2510.07677
"Some super-approximation rates of ReLU neural networks for Korobov functions", arXiv:2507.10345
"Higher order approximation rates for ReLU CNNs in Korobov spaces", arXiv:2501.11275
"Some new convergence analysis and applications of POD-greedy algorithms", arXiv:2407.09933
"Nodal auxiliary a posteriori error estimates", Mathematics of Computation, arXiv:2010.06774, DOI: 10.1090/mcom/4141
"A new rational approximation algorithm via the empirical interpolation method", SIAM Journal on Scientific Computing, Vol. 47, No. 5, (2025) A2559-A2582.
"Reduced Krylov basis methods for parametric partial differential equations", SIAM Journal on Numerical Analysis, Vol. 63, No. 2, (2025) 976-999.
"A new analysis of empirical interpolation methods and Chebyshev greedy algorithms", SIAM Journal on Numerical Analysis, Vol. 63, No. 2, (2025) 931-948.
"A reduced conjugate gradient basis method for fractional diffusion", SIAM Journal on Scientific Computing, S68-S87 (2024)
"Entropy-based convergence rates for greedy algorithms", Mathematical Models and Methods in Applied Sciences, Vol. 34, No. 5 (2024) 779-802.
"Paramter-free preconditioning for nearly incompressible linear elasticity", Computers&Mathematics with Applications, 154 (2024) 39-44.
"Nodal auxiliary space preconditioning for the surface de Rham complex", Foundations of Computational Mathematics, Vol. 24 (2024) 1019-1048.
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