Home Research Publications Teaching Contacts Shukai Du's Website

Publications

Publications

Submitted

  1. B. Cockburn, S. Du, M. A. Sánchez. A spectral analysis of hp-hybridized mixed and HDG methods for parametric second-order elliptic problems.
  2. S. Du, T. Le, S. N. Stechmann. Element learning with hp-adaptivity: machine learning-based acceleration of hp-adaptive spectral element methods, and application to atmospheric radiative transfer.

Peer-reviewed

  1. J. L. Torchinsky, S. Du, and S. N. Stechmann. Angular-spatial hp-adaptivity for radiative transfer with discontinuous Galerkin spectral element methods.
    J. Quant. Spectrosc. Radiat. Transf. 348 (2026). DOI: 10.1016/j.jqsrt.2025.109687
  2. D. H. Marsico, S. Du, and S. N. Stechmann. Can second-order numerical accuracy be achieved for moist atmospheric dynamics with non-smoothness at cloud edge?
    J. Adv. Model. Earth Syst. 17 (2025). DOI: 10.1029/2025MS005293
  3. S. Du, and S. N. Stechmann. Element learning: a systematic approach of accelerating finite element-type methods via machine learning, with applications to radiative transfer.
    J. Comput. Math. (2024). DOI: 10.4208/jcm.2407-m2024-0047
  4. S. Du, and S. N. Stechmann. Inverse radiative transfer with goal-oriented hp-adaptive mesh refinement: adaptive-mesh inversion.
    Inverse Probl. 39 (2023), no. 11. DOI: 10.1088/1361-6420/acf785
  5. B. Cockburn, S. Du, and M. A. Sánchez. A priori error analysis of new semidiscrete, Hamiltonian HDG methods for the time-dependent Maxwell's equations.
    ESAIM: M2AN 57 (2023), no. 4, 2097 – 2129. DOI: 10.1051/m2an/2023048
  6. S. Du, and S. N. Stechmann. Fast, low-memory numerical methods for radiative transfer via hp-adaptive mesh refinement.
    J. Comput. Phys. 480 (2023). DOI: 10.1016/j.jcp.2023.112021
  7. S. Du, and S. N. Stechmann. A universal predictor-corrector approach for minimizing artifacts due to mesh refinement.
    J. Adv. Model. Earth Syst. 15 (2023). DOI: 10.1029/2023MS003688
  8. B. Cockburn, S. Du, and M. A. Sánchez. Combining finite element space-discretization with symplectic time-marching schemes for linear Hamiltonian systems.
    Front. Appl. Math. Stat. 9 (2023). DOI: 10.3389/fams.2023.1165371
  9. M. A. Sánchez, S. Du, B. Cockburn, N.-C. Nguyen, J. Peraire. Symplectic Hamiltonian finite element methods for electromagnetics.
    Comput. Methods Appl. Mech. Engrg. 396 (2022). DOI: 10.1016/j.cma.2022.114969
  10. B. Cockburn, M. A. Sánchez, S. Du. Discontinuous Galerkin methods with time-operators in their numerical traces for time-dependent electromagnetics.
    Comput. Meth. Appl. Math. 22 (2022), no. 4, 775-796. DOI: 10.1515/cmam-2021-0215
  11. S. Du, and F.-J. Sayas. A note on devising HDG+ projections on polyhedral elements.
    Math. Comp. 90 (2021), 65-79. DOI: 10.1090/mcom/3573
  12. S. Du. HDG methods for the Stokes equation based on strong symmetric stress formulations.
    J. Sci. Comput. 85 (2020), 8. DOI: 10.1007/s10915-020-01309-7
  13. S. Du, and F.-J. Sayas. A unified error analysis of hybridizable discontinuous Galerkin methods for the static Maxwell equations.
    SIAM J. Numer. Anal. 58 (2020), no. 2, 1367–1391. DOI: 10.1137/19M1290966
  14. S. Du, and F.-J. Sayas. New analytical tools for HDG in elasticity, with applications to elastodynamics.
    Math. Comp. 89 (2020), 1745-1782. DOI: 10.1090/mcom/3499
  15. S. Du, and N. Du. A factorization of least-squares projection schemes for ill-posed problems.
    Comput. Meth. Appl. Math. 20 (2020), no. 4, 783-798. DOI: 10.1515/cmam-2019-0173
  16. T.S. Brown, S. Du, H. Eruslu, and F.-J. Sayas. Analysis of models for viscoelastic wave propagation.
    Appl. Math. Nonlin. Sci. 3 (2018), no. 1, 55-96. DOI: 10.21042/AMNS.2018.1.00006

Books

  1. S. Du, and F.-J. Sayas. An invitation to the theory of the Hybridizable Discontinuous Galerkin Method.
    SpringerBriefs Math. (2019). DOI: 10.1007/978-3-030-27230-2