Publications

2025

1. arXiv

   Design and analysis of twisted and BGG Stokes-de Rham polytopal complexes

   Daniele A Di Pietro, Jérôme Droniou, Kaibo Hu, and 1 more author

   arXiv preprint arXiv:2507.17333, 2025

   Bib HTML

   @article{di2025design,
     title = {Design and analysis of twisted and BGG Stokes-de Rham polytopal complexes},
     author = {Di Pietro, Daniele A and Droniou, J{\'e}r{\^o}me and Hu, Kaibo and Leroy, Arax},
     journal = {arXiv preprint arXiv:2507.17333},
     year = {2025}
   }

2. arXiv

   A 2-complex containing Sobolev spaces of matrix fields

   Jay Gopalakrishnan, Kaibo Hu, and Joachim Schöberl

   arXiv preprint arXiv:2507.11869, 2025

   Bib HTML

   @article{gopalakrishnan20252,
     title = {{A 2-complex containing Sobolev spaces of matrix fields}},
     author = {Gopalakrishnan, Jay and Hu, Kaibo and Sch{\"o}berl, Joachim},
     journal = {arXiv preprint arXiv:2507.11869},
     year = {2025}
   }

3. arXiv

   Convergence and Stability of Discrete Exterior Calculus for the Hodge Laplace Problem in Two Dimensions

   Chengbin Zhu, Snorre H. Christiansen, Kaibo Hu, and 1 more author

   arXiv preprint arXiv:2505.08966, 2025

   Bib HTML

   @article{DEC2025,
     title = {Convergence and Stability of Discrete Exterior Calculus for the Hodge Laplace Problem in Two Dimensions},
     author = {Zhu, Chengbin and Christiansen, Snorre H. and Hu, Kaibo and Hirani, Anil N.},
     journal = {arXiv preprint arXiv:2505.08966},
     year = {2025}
   }

4. arXiv

   Many facets of cohomology: Differential complexes and structure-aware formulations

   Kaibo Hu

   arXiv preprint arXiv:2503.22813, 2025

   Bib HTML

   @article{rssurvey2025,
     title = {Many facets of cohomology: Differential complexes and structure-aware formulations},
     author = {Hu, Kaibo},
     journal = {arXiv preprint arXiv:2503.22813},
     year = {2025}
   }

5. arXiv

   Finite element form-valued forms: Construction

   Kaibo Hu, and Ting Lin

   arXiv preprint arXiv:2503.03243, 2025

   Bib HTML

   @article{hu2024intrinsic,
     title = {Finite element form-valued forms: Construction},
     author = {Hu, Kaibo and Lin, Ting},
     journal = {arXiv preprint arXiv:2503.03243},
     year = {2025}
   }

6. arXiv

   Topology-preserving discretization for the magneto-frictional equations arising in the Parker conjecture

   Mingdong He, Patrick E Farrell, Kaibo Hu, and 1 more author

   arXiv preprint arXiv:2501.11654, 2025

   Bib HTML

   @article{he2025topology,
     title = {Topology-preserving discretization for the magneto-frictional equations arising in the Parker conjecture},
     author = {He, Mingdong and Farrell, Patrick E and Hu, Kaibo and Andrews, Boris D},
     journal = {arXiv preprint arXiv:2501.11654},
     year = {2025}
   }

7. SINUM

   Intrinsic Mixed Finite Element Methods for Linear Cosserat Elasticity

   Andrea Dziubek, Kaibo Hu, Michael Karow, and 1 more author

   SIAM Journal on Numerical Analysis, 2025

   Bib

   @article{dziubek2025intrinsic,
     title = {Intrinsic Mixed Finite Element Methods for Linear Cosserat Elasticity},
     author = {Dziubek, Andrea and Hu, Kaibo and Karow, Michael and Neunteufel, Michael},
     journal = {SIAM Journal on Numerical Analysis},
     volume = {63},
     number = {4},
     pages = {1833--1860},
     year = {2025},
     publisher = {SIAM}
   }

8. ESAIM

   Error estimates for a helicity-preserving finite element discretisation of an incompressible magnetohydrodynamics system

   Lourenco Beirao Da Veiga, Kaibo Hu, and Lorenzo Mascotto

   ESAIM: Mathematical Modelling and Numerical Analysis, 2025

   Bib HTML

   @article{da2025error,
     title = {Error estimates for a helicity-preserving finite element discretisation of an incompressible magnetohydrodynamics system},
     author = {Da Veiga, Lourenco Beirao and Hu, Kaibo and Mascotto, Lorenzo},
     journal = {ESAIM: Mathematical Modelling and Numerical Analysis},
     volume = {59},
     number = {2},
     pages = {1075--1094},
     year = {2025},
     publisher = {EDP Sciences}
   }

9. MNS

   Intrinsic finite elements: currents, discrete geometry and periodic table (in Chinese)

   Kaibo Hu

   Mathematica Numerica Sinica (Young Researcher Review), 2025

   Bib HTML

   @article{chinese-survey,
     title = {Intrinsic finite elements: currents,  discrete geometry and periodic table (in Chinese)},
     author = {Hu, Kaibo},
     journal = {Mathematica Numerica Sinica (Young Researcher Review)},
     volume = {47},
     number = {3},
     pages = {385-417},
     url = {https://computmath.cjoe.ac.cn/jssx/CN/10.12286/jssx.j2025-1308},
     year = {2025}
   }

10. SIAGA

    Distributional Hessian and divdiv complexes on triangulation and cohomology

    Kaibo Hu, Ting Lin, and Qian Zhang

    accepted, SIAM Journal on Applied Algebra and Geometry, 2025

    Bib HTML

    @article{hu2023distributional,
      title = {Distributional Hessian and divdiv complexes on triangulation and cohomology},
      author = {Hu, Kaibo and Lin, Ting and Zhang, Qian},
      journal = {accepted, SIAM Journal on Applied Algebra and Geometry},
      year = {2025}
    }

11. JEMS

    An exterior calculus framework for polytopal methods

    Francesco Bonaldi, Daniele A Di Pietro, Jérôme Droniou, and 1 more author

    Journal of the European Mathematical Society, 2025

    Bib HTML

    @article{bonaldi2023exterior,
      title = {An exterior calculus framework for polytopal methods},
      author = {Bonaldi, Francesco and Di Pietro, Daniele A and Droniou, J{\'e}r{\^o}me and Hu, Kaibo},
      journal = {Journal of the European Mathematical Society},
      year = {2025},
    }

2024

1. arXiv

   Uniformly hp -stable elements for the elasticity complex

   Francis RA Aznaran, Kaibo Hu, and Charles Parker

   arXiv preprint arXiv:2409.17414, 2024

   Bib HTML

   @article{aznaran2024uniformly,
     title = {Uniformly $ hp $-stable elements for the elasticity complex},
     author = {Aznaran, Francis RA and Hu, Kaibo and Parker, Charles},
     journal = {arXiv preprint arXiv:2409.17414},
     year = {2024}
   }

2. RINAM

   Quadratic and cubic Lagrange finite elements for mixed Laplace eigenvalue problems on criss-cross meshes

   Kaibo Hu, Jiguang Sun, and Qian Zhang

   Results in Applied Mathematics, 2024

   Bib HTML

   @article{hu2024quadratic,
     title = {Quadratic and cubic Lagrange finite elements for mixed Laplace eigenvalue problems on criss-cross meshes},
     author = {Hu, Kaibo and Sun, Jiguang and Zhang, Qian},
     journal = {Results in Applied Mathematics},
     volume = {23},
     pages = {100480},
     url = {https://www.sciencedirect.com/science/article/pii/S2590037424000505},
     year = {2024},
     publisher = {Elsevier}
   }

2023

1. arXiv

   Finite elements for symmetric and traceless tensors in three dimensions

   Kaibo Hu, Ting Lin, and Bowen Shi

   arXiv preprint arXiv:2311.16077, 2023

   Bib HTML

   @article{hu2023finite,
     title = {Finite elements for symmetric and traceless tensors in three dimensions},
     author = {Hu, Kaibo and Lin, Ting and Shi, Bowen},
     journal = {arXiv preprint arXiv:2311.16077},
     year = {2023}
   }

2. FoCM

   BGG sequences with weak regularity and applications

   Andreas Čap, and Kaibo Hu

   Foundations of Computational Mathematics, 2023

   Bib HTML

   @article{vcap2023bgg,
     title = {BGG sequences with weak regularity and applications},
     author = {{\v{C}}ap, Andreas and Hu, Kaibo},
     journal = {Foundations of Computational Mathematics},
     pages = {1--40},
     year = {2023},
     publisher = {Springer},
     url = {https://link.springer.com/article/10.1007/s10208-023-09608-9},
   }

3. FoCM

   Finite element systems for vector bundles: elasticity and curvature

   Snorre H Christiansen, and Kaibo Hu

   Foundations of Computational Mathematics, 2023

   Bib HTML

   @article{christiansen2023finite,
     title = {Finite element systems for vector bundles: elasticity and curvature},
     author = {Christiansen, Snorre H and Hu, Kaibo},
     journal = {Foundations of Computational Mathematics},
     volume = {23},
     number = {2},
     pages = {545--596},
     year = {2023},
     publisher = {Springer},
     url = {https://link.springer.com/article/10.1007/s10208-022-09555-x},
   }

4. arXiv

   A discrete elasticity complex on three-dimensional Alfeld splits

   Snorre H Christiansen, Jay Gopalakrishnan, Johnny Guzmán, and 1 more author

   accepted, Numerische Mathematik, 2023

   Bib HTML

   @article{christiansen2020discrete,
     title = {A discrete elasticity complex on three-dimensional Alfeld splits},
     author = {Christiansen, Snorre H and Gopalakrishnan, Jay and Guzm{\'a}n, Johnny and Hu, Kaibo},
     journal = {accepted, Numerische Mathematik},
     year = {2023},
   }

5. arXiv

   Discrete tensor product BGG sequences: splines and finite elements

   Francesca Bonizzoni, Kaibo Hu, Guido Kanschat, and 1 more author

   arXiv preprint arXiv:2302.02434, 2023

   Bib HTML

   @article{bonizzoni2023discrete,
     title = {Discrete tensor product BGG sequences: splines and finite elements},
     author = {Bonizzoni, Francesca and Hu, Kaibo and Kanschat, Guido and Sap, Duygu},
     journal = {arXiv preprint arXiv:2302.02434},
     year = {2023},
   }

6. JCP

   Structure-preserving and helicity-conserving finite element approximations and preconditioning for the Hall MHD equations

   Fabian Laakmann, Kaibo Hu, and Patrick E Farrell

   Journal of Computational Physics, 2023

   Bib HTML

   @article{laakmann2023structure,
     title = {Structure-preserving and helicity-conserving finite element approximations and preconditioning for the Hall MHD equations},
     author = {Laakmann, Fabian and Hu, Kaibo and Farrell, Patrick E},
     journal = {Journal of Computational Physics},
     pages = {112410},
     year = {2023},
     publisher = {Elsevier},
     url = {https://www.sciencedirect.com/science/article/abs/pii/S0021999123005053},
   }

7. IMA

   Spurious solutions for high-order curl problems

   Kaibo Hu, Qian Zhang, Jiayu Han, and 2 more authors

   IMA Journal of Numerical Analysis, 2023

   Bib HTML

   @article{hu2023spurious,
     title = {Spurious solutions for high-order curl problems},
     author = {Hu, Kaibo and Zhang, Qian and Han, Jiayu and Wang, Lixiu and Zhang, Zhimin},
     journal = {IMA Journal of Numerical Analysis},
     volume = {43},
     number = {3},
     pages = {1422--1449},
     year = {2023},
     publisher = {Oxford University Press},
   }

8. arXiv

   Nonlinear elasticity complex and a finite element diagram chase

   Kaibo Hu

   to appear in Springer INdAM Series “Approximation Theory and Numerical Analysis Meet Algebra, Geometry, Topology”, edited by Martina Lanini, Henry Schenck. Carla Manni. , 2023

   Bib HTML

   @article{hu2023nonlinear,
     title = {Nonlinear elasticity complex and a finite element diagram chase},
     author = {Hu, Kaibo},
     journal = {to appear in Springer INdAM Series “Approximation Theory and Numerical Analysis Meet Algebra, Geometry, Topology”, edited by Martina Lanini, Henry Schenck. Carla Manni.
     },
     year = {2023},
   }

9. arXiv

   Supersmoothness of the Alfeld split

   Michael S. Floater, and Kaibo Hu

   to appear in Springer INdAM Series “Approximation Theory and Numerical Analysis Meet Algebra, Geometry, Topology”, edited by Martina Lanini, Henry Schenck. Carla Manni. , 2023

   Bib

   @article{cortona-supersmoothness,
     title = {Supersmoothness of the Alfeld split},
     author = {Floater, Michael S. and Hu, Kaibo},
     journal = {to appear in Springer INdAM Series “Approximation Theory and Numerical Analysis Meet Algebra, Geometry, Topology”, edited by Martina Lanini, Henry Schenck. Carla Manni.
     },
     year = {2023},
   }

10. JMPA

    Bounded Poincaré operators for twisted and BGG complexes

    Andreas Čap, and Kaibo Hu

    accepted, Journal de mathématiques pures et appliquées, 2023

    Bib HTML

    @article{vcap2023bounded,
      title = {Bounded Poincar\'e operators for twisted and BGG complexes},
      author = {{\v{C}}ap, Andreas and Hu, Kaibo},
      journal = {accepted, Journal de mathématiques pures et appliquées},
      year = {2023},
    }

2022

1. SINUM

   A family of finite element Stokes complexes in three dimensions

   Kaibo Hu, Qian Zhang, and Zhimin Zhang

   SIAM Journal on Numerical Analysis, 2022

   Bib HTML

   @article{hu2022family,
     title = {A family of finite element Stokes complexes in three dimensions},
     author = {Hu, Kaibo and Zhang, Qian and Zhang, Zhimin},
     journal = {SIAM Journal on Numerical Analysis},
     volume = {60},
     number = {1},
     pages = {222--243},
     year = {2022},
     publisher = {SIAM},
     url = {https://epubs.siam.org/doi/abs/10.1137/20M1358700},
   }

2. arXiv

   Oberwolfach report: Discretization of Hilbert complexes

   Kaibo Hu

   arXiv preprint arXiv:2208.03420, 2022

   Bib HTML

   @article{hu2022oberwolfach,
     title = {Oberwolfach report: Discretization of Hilbert complexes},
     author = {Hu, Kaibo},
     journal = {arXiv preprint arXiv:2208.03420},
     year = {2022},
   }

3. CMAM

   Partially Discontinuous Nodal Finite Elements for 𝐻(curl) and 𝐻(div)

   Jun Hu, Kaibo Hu, and Qian Zhang

   Computational Methods in Applied Mathematics, 2022

   Bib HTML

   @article{hu2022partially,
     title = {Partially Discontinuous Nodal Finite Elements for 𝐻(curl) and 𝐻(div)},
     author = {Hu, Jun and Hu, Kaibo and Zhang, Qian},
     journal = {Computational Methods in Applied Mathematics},
     volume = {22},
     number = {3},
     pages = {613--629},
     year = {2022},
     publisher = {De Gruyter},
   }

2021

1. FoCM

   Complexes from complexes

   Douglas N Arnold, and Kaibo Hu

   Foundations of Computational Mathematics, 2021

   Bib HTML

   @article{arnold2021complexes,
     title = {Complexes from complexes},
     author = {Arnold, Douglas N and Hu, Kaibo},
     journal = {Foundations of Computational Mathematics},
     volume = {21},
     number = {6},
     pages = {1739--1774},
     year = {2021},
     publisher = {Springer},
     url = {https://link.springer.com/article/10.1007/s10208-021-09498-9},
   }

2. JCP

   Helicity-conservative finite element discretization for incompressible MHD systems

   Kaibo Hu, Young-Ju Lee, and Jinchao Xu

   Journal of Computational Physics, 2021

   Bib HTML

   @article{hu2021helicity,
     title = {Helicity-conservative finite element discretization for incompressible MHD systems},
     author = {Hu, Kaibo and Lee, Young-Ju and Xu, Jinchao},
     journal = {Journal of Computational Physics},
     volume = {436},
     pages = {110284},
     year = {2021},
     publisher = {Elsevier},
     url = {https://www.sciencedirect.com/science/article/abs/pii/S0021999121001790},
   }

3. JCM

   Well-conditioned frames for high order finite element methods

   Kaibo Hu, and Ragnar Winther

   Journal of Computational Mathematics, 2021

   Bib HTML

   @article{hu2017well,
     title = {Well-conditioned frames for high order finite element methods},
     author = {Hu, Kaibo and Winther, Ragnar},
     journal = {Journal of Computational Mathematics},
     year = {2021},
     volume = {39},
     number = {3},
     pages = {333--357},
   }

2020

1. SISC

   Simple curl-curl-conforming finite elements in two dimensions

   Kaibo Hu, Qian Zhang, and Zhimin Zhang

   SIAM Journal on Scientific Computing, 2020

   Bib HTML

   @article{hu2020simple,
     title = {Simple curl-curl-conforming finite elements in two dimensions},
     author = {Hu, Kaibo and Zhang, Qian and Zhang, Zhimin},
     journal = {SIAM Journal on Scientific Computing},
     volume = {42},
     number = {6},
     pages = {A3859--A3877},
     year = {2020},
     publisher = {SIAM},
     url = {https://epubs.siam.org/doi/abs/10.1137/20M1333390},
   }

2. ACM

   A characterization of supersmoothness of multivariate splines

   Michael S Floater, and Kaibo Hu

   Advances in Computational Mathematics, 2020

   Bib HTML

   @article{floater2020characterization,
     title = {A characterization of supersmoothness of multivariate splines},
     author = {Floater, Michael S and Hu, Kaibo},
     journal = {Advances in Computational Mathematics},
     volume = {46},
     number = {5},
     pages = {70},
     year = {2020},
     publisher = {Springer},
     url = {https://link.springer.com/article/10.1007/s10444-020-09813-y},
   }

3. JCAM

   Convergence of a BE based finite element method for MHD models on Lipschitz domains

   Kaibo Hu, Weifeng Qiu, and Ke Shi

   Journal of Computational and Applied Mathematics, 2020

   Bib HTML

   @article{hu2020convergence,
     title = {Convergence of a BE based finite element method for MHD models on Lipschitz domains},
     author = {Hu, Kaibo and Qiu, Weifeng and Shi, Ke},
     journal = {Journal of Computational and Applied Mathematics},
     volume = {368},
     pages = {112477},
     year = {2020},
     publisher = {Elsevier},
     url = {https://www.sciencedirect.com/science/article/abs/pii/S0377042719304807},
   }

4. JMPA

   Poincaré path integrals for elasticity

   Snorre H Christiansen, Kaibo Hu, and Espen Sande

   Journal de Mathématiques Pures et Appliquées, 2020

   Bib HTML

   @article{christiansen2020poincare,
     title = {Poincar{\'e} path integrals for elasticity},
     author = {Christiansen, Snorre H and Hu, Kaibo and Sande, Espen},
     journal = {Journal de Math{\'e}matiques Pures et Appliqu{\'e}es},
     volume = {135},
     pages = {83--102},
     year = {2020},
     publisher = {Elsevier},
     url = {https://www.sciencedirect.com/science/article/abs/pii/S0021782419301187},
   }

5. BIT

   Nonstandard finite element de Rham complexes on cubical meshes

   Andrew Gillette, Kaibo Hu, and Shuo Zhang

   BIT Numerical Mathematics, 2020

   Bib HTML

   @article{gillette2020nonstandard,
     title = {Nonstandard finite element de Rham complexes on cubical meshes},
     author = {Gillette, Andrew and Hu, Kaibo and Zhang, Shuo},
     journal = {BIT Numerical Mathematics},
     volume = {60},
     pages = {373--409},
     year = {2020},
     publisher = {Springer},
     url = {https://link.springer.com/article/10.1007/s10543-019-00779-y},
   }

2019

1. Math.Comp.

   Structure-preserving finite element methods for stationary MHD models

   Kaibo Hu, and Jinchao Xu

   Mathematics of Computation, 2019

   Bib HTML

   @article{hu2019structure,
     title = {Structure-preserving finite element methods for stationary MHD models},
     author = {Hu, Kaibo and Xu, Jinchao},
     journal = {Mathematics of Computation},
     volume = {88},
     number = {316},
     pages = {553--581},
     year = {2019},
     url = {https://www.ams.org/mcom/2019-88-316/S0025-5718-2018-03341-5/},
   }

2. Num.Math.

   Generalized Gaffney inequality and discrete compactness for discrete differential forms

   Juncai He, Kaibo Hu, and Jinchao Xu

   Numerische Mathematik, 2019

   Bib HTML

   @article{he2019generalized,
     title = {Generalized Gaffney inequality and discrete compactness for discrete differential forms},
     author = {He, Juncai and Hu, Kaibo and Xu, Jinchao},
     journal = {Numerische Mathematik},
     volume = {143},
     number = {4},
     pages = {781--795},
     year = {2019},
     publisher = {Springer},
     url = {https://link.springer.com/article/10.1007/s00211-019-01076-0},
   }

2018

1. Num.Math.

   Generalized finite element systems for smooth differential forms and Stokes’ problem

   Snorre H Christiansen, and Kaibo Hu

   Numerische Mathematik, 2018

   Bib HTML

   @article{christiansen2018generalized,
     title = {Generalized finite element systems for smooth differential forms and Stokes’ problem},
     author = {Christiansen, Snorre H and Hu, Kaibo},
     journal = {Numerische Mathematik},
     volume = {140},
     pages = {327--371},
     year = {2018},
     publisher = {Springer},
     url = {https://link.springer.com/article/10.1007/s00211-018-0970-6},
   }

2. Num.Math.

   Nodal finite element de Rham complexes

   Snorre H Christiansen, Jun Hu, and Kaibo Hu

   Numerische Mathematik, 2018

   Bib HTML

   @article{christiansen2018nodal,
     title = {Nodal finite element de Rham complexes},
     author = {Christiansen, Snorre H and Hu, Jun and Hu, Kaibo},
     journal = {Numerische Mathematik},
     volume = {139},
     number = {2},
     pages = {411--446},
     year = {2018},
     publisher = {Springer},
     url = {https://link.springer.com/article/10.1007/s00211-017-0939-x},
   }

2017

1. Num.Math.

   Stable finite element methods preserving ∇⋅B=0 exactly for MHD models

   Kaibo Hu, Yicong Ma, and Jinchao Xu

   Numerische Mathematik, 2017

   Bib HTML

   @article{hu2017stable,
     title = {Stable finite element methods preserving $\nabla\cdot {B}=0$ exactly for MHD models},
     author = {Hu, Kaibo and Ma, Yicong and Xu, Jinchao},
     journal = {Numerische Mathematik},
     volume = {135},
     number = {2},
     pages = {371--396},
     year = {2017},
     publisher = {Springer},
     url = {https://link.springer.com/article/10.1007/s00211-016-0803-4},
   }

2016

1. JCP

   Robust preconditioners for incompressible MHD models

   Yicong Ma, Kaibo Hu, Xiaozhe Hu, and 1 more author

   Journal of Computational Physics, 2016

   Bib HTML

   @article{ma2016robust,
     title = {Robust preconditioners for incompressible MHD models},
     author = {Ma, Yicong and Hu, Kaibo and Hu, Xiaozhe and Xu, Jinchao},
     journal = {Journal of Computational Physics},
     volume = {316},
     pages = {721--746},
     year = {2016},
     publisher = {Elsevier},
     url = {https://www.sciencedirect.com/science/article/pii/S0021999116300602},
   }

2. Sci.China

   磁流体动力学方程组的稳定磁场-电流有限元格式

   胡凯博, and  许进超

   中国科学: 数学, 2016

   Bib HTML

   @article{mhd-chinese,
     title = {磁流体动力学方程组的稳定磁场-电流有限元格式},
     author = {胡凯博 and 许进超},
     journal = {中国科学: 数学},
     number = {7},
     pages = {967--980},
     year = {2016},
   }