S. Bertoluzza, E. Burman, and C. He*,
"Best approximation results and essential boundary conditions for novel types of weak adversarial network discretizations for PDEs."
SIAM Journal of Scientific Computation (2nd Revision). arXiv preprint: arXiv:2307.05012 (2023).
C. Capatina*., A. Gouasmi and C. He,
"Robust flux reconstruction and a posteriori error analysis for an elliptic problem with discontinuous coefficients}, (accepted)"
Journal of Scientific Computing (2023).
X. Xie, Y. Wu, H. Ni and C. He*,
"NODE-ImgNet: a PDE-informed effective and robust model for image denoising",
Pattern Recognition (2023). https://doi.org/10.1016/j.patcog.2023.110176
Z. Wilson A.*, C. He, and B. A. Zambrano-Luna,
"p-Adic Statistical Field Theory and Convolutional Deep Boltzmann Machines",
Progress of Theoretical and Experimental Physics (2023)", https://doi.org/10.1093/ptep/ptad061.
C. He*, S. Zhang, and X. Zhang, "Error Analysis of Petrov Galerkin immersed Finite Element Methods",
Computer Methods in Applied Mechanics and Engineering, (2022), https://doi.org/10.1016/j.cma.2022.115744
Paul Valsecchi Oliva, Yue Wu, Cuiyu He and Hao Ni*. " Towards fast weak adversarial training to solve high dimensional parabolic partial differential equations using XNODE-WAN". Journal of Computational Physics, (2022). https://doi.org/10.1016/j.jcp.2022.111233
Cuiyu He, Xiaozhe Hu, and Lin Mu. "A Mesh-free Method Using Piecewise Deep Neural Network for Elliptic Interface Problems."
Journal of Computational and Applied Mathematics (2021)}, https://doi.org/10.1016/j.cam.2022.114358
Daniela Capatina and Cuiyu He, "Flux recovery for Cut finite element method and its application in a posteriori error estimation",
ESAIM: Mathematical Modelling and Numerical Analysis, (2021). In press. https://arxiv.org/abs/2005.04847
Silvia, Bertoluzza, Erik Burman, and Cuiyu He. "An a posteriori error estimate of the outer normal derivative using dual weights." SIAM Journal on Numerical Analysis, (2021). In press. https://arxiv.org/abs/2008.07690
Cuiyu He, Zhiqiang Cai, and Shun Zhang. "Generalized Prager-Synge Inequality and Equilibrated Error Estimators for Discontinuous Elements." Computational and Applied Mathematics (2021), https://doi.org/10.1016/j.cam.2021.113673.
Erik Burman, Cuiyu He, and Mats G. Larson. "Comparison of Shape Derivatives using CutFEM for Ill-posed Bernoulli Free Boundary Problem." Journal of Scientific Computing (2021), https://doi.org/10.1007/s10915-021-01544-6
Cuiyu He, Weiwei Hu, and Lin Mu. "Optimal Control of Convection-Cooling and Numerical Implementation." Computers and Mathematics with Applications (2021), https://doi.org/10.1016/j.camwa.2021.03.020.
Cai, Zhiqiang, Cuiyu He, and Shun Zhang. "Improved ZZ a posteriori error estimators for diffusion problems: Discontinuous elements." Applied Numerical Mathematics (2020).
Burman, Erik, Cuiyu He, and Mats G. Larson. "A Posteriori Error Estimates with Boundary Correction for a Cut Finite Element Method." IMA Journal of Numerical Analysis (2020). https://doi.org/10.1093/imanum/draa085
Burman, Erik, and Cuiyu He. "Primal dual mixed finite element methods for indefinite advection-diffusion equations." SIAM Journal on Numerical Analysis 57.6 (2019): 2785-2811.
He, Cuiyu, and Xu Zhang. "Residual-based a posteriori error estimation for immersed finite element methods." Journal of Scientific Computing 81.3 (2019): 2051-2079.
Zhiqiang Cai, Cuiyu He, and Shun Zhang. "Residual-based a posteriori error estimate for interface problems: Nonconforming linear elements." Mathematics of Computation 86.304 (2017): 617-636.
Zhiqiang Cai, Cuiyu He, and Shun Zhang. "Discontinuous finite element methods for interface problems: Robust a priori and a posteriori error estimates." SIAM Journal on Numerical Analysis 55.1 (2017): 400-418.
Zhiqiang Cai, Cuiyu He, and Shun Zhang. "Improved ZZ a posteriori error estimators for diffusion problems: Conforming linear elements." Computer Methods in Applied Mechanics and Engineering 313 (2017): 433-449.