Publications

Articles in peer-reviewed journals​

1. A. Cangiani, Z. Dong, E. H. Georgoulis, and P. Houston.  

hp–Version discontinuous Galerkin methods for advection-diffusion-reaction problems on polytopic meshes. ESAIM: Mathematical Modelling and Numerical Analysis. 50(3) pp. 699-725, (2016).  (Preprint Link)

2. A. Cangiani, Z. Dong, and E. H. Georgoulis.

hp–Version space-time discontinuous Galerkin methods for parabolic problems on prismatic meshes. SIAM Journal on Scientific Computing. 39(4) pp.A1251–A1279 (2017). (ArXiv Link)

3. Z. Dong, E. H. Georgoulis, J. Levesley, and F. Usta.

A multilevel sparse kernel-based stochastic collocation finite element method for elliptic problems with random coefficients. Computers and Mathematics with Applications., 76(8) pp.A1950-A1965 (2018).

4. Z. Dong.

On the exponent of exponential convergence of p-version finite element spaces. Advances in Computational Mathematics., 45(2) pp.757–785(2019). (ArXiv Link)

5. Z. Dong.

Discontinuous Galerkin methods for the biharmonic problem on polygonal and polyhedral meshes. International Journal of Numerical Analysis and Modeling.,16(5) pp.825-846 (2019). (ArXiv Link)

6. Z. Dong, E. H. Georgoulis, and T. Pryer.

Recovered finite element methods on polygonal and polyhedral meshes. ESAIM: Mathematical Modeling and Numerical Analysis, Vol. 54(4), 1309 - 1337 (2020).  (ArXiv Link) 

7. Z. Dong, L. Mascotto, and O. J. Sutton.

Residual-based a posteriori error estimates for hp-discontinuous Galerkin discretisations of the biharmonic problem. SIAM Journal on Numerical Analysis, 59(3), 1273–1298 (2021).  (ArXiv Link) (Hal Link)

8. Z. Dong, E. H. Georgoulis, and T. Kappas.

GPU-accelerated discontinuous Galerkin methods on polytopic meshes. SIAM Journal on Scientific Computing, 43(4), C312–C334 (2021). (ArXiv Link) (Hal Link)

9. A. Cangiani, Z. Dong, and E. H. Georgoulis.

hp–Version discontinuous Galerkin methods on essentially arbitrarily-shaped elements. Mathematics of Computation, 91(333) (2021), 1-35. (ArXiv Link) (Hal Link)

10. Z. Dong, and A. Ern

Hybrid high-order method for singularly perturbed fourth-order problems on curved domains. ESAIM: Mathematical Modeling and Numerical Analysis, 55(6),3091-3114 (2021). (ArXiv Link) (Hal Link)

11. Z. Dong, and A. Ern

Hybrid high-order and weak Galerkin methods for the biharmonic problem. SIAM Journal on Numerical Analysis, 60(5), 2626–2656 (2022). (ArXiv Link) (Hal Link)

12. Z. Dong, and E. H. Georgoulis

Robust interior penalty discontinuous Galerkin methods. Journal of Scientific Computing, 92(57) (2022). (ArXiv Link) (Hal Link)

13. Z. Dong, A. Ern, and J.-L. Guermond

Local decay rates of best-approximation errors using vector-valued finite elements for fields with low regularity and integrable curl or divergence. Comptes Rendus. Mathématique, Volume 361 (2023), pp. 723-736. (ArXiv Link) (Hal Link)

14. Z. Dong, and L. Mascotto.

hp-optimal interior penalty discontinuous Galerkin methods for the biharmonic problem. Journal of Scientific Computing, 96(30) (2023).  (ArXiv Link) (Hal Link)

15. Z. Dong, M. Hauck and R. Maier.

An improved high-order method for elliptic multiscale problems. SIAM Journal on Numerical Analysis.  61(4), 1918–1937 (2023).  (ArXiv Link) (Hal Link)

16. A. Cangiani, Z. Dong, and E. H. Georgoulis.

A posteriori error estimates for discontinuous Galerkin methods on polygonal and polyhedral meshes. SIAM Journal on Numerical Analysis.  61(5), 2352--2380 (2023).  (ArXiv Link) (Hal Link)

17. Z. Dong, and A. Ern

C^0-hybrid high-order methods for biharmonic problems. IMA Journal of Numerical Analysis, 2024, 44 (1), pp.24-57. (ArXiv Link) (Hal Link)

18. Z. Dong and L. Mascotto.

hp-optimal convergence of the original DG method for linear hyperbolic problems on special simplicial meshes. Submitted for publication.  (ArXiv Link) (Hal Link)

19. Z. Dong, E. H. Georgoulis. and P. J. Herbert.

A hypocoercivity-exploiting stabilised finite element method for Kolmogorov equation. Submitted for publication. (ArXiv Link) (Hal Link)

20. D. A. Di Pietro, Z. Dong , G. Kanschat, P. Matalon and A. Rupp.

Homogeneous multigrid for hybrid discretizations: application to HHO methods. Submitted for publication. (ArXiv Link) (Hal Link)

Chapters in peer-Contributions in conference proceedings

1. Z. Dong and L. Mascotto.

On the suboptimality of the p-version discontinuous Galerkin methods for first order hyperbolic problems. 14th WCCM-ECCOMAS Congress 2020. Vol. 700 (2021). (Arixv Link) (Hal Link)

2. Z. Dong and Z. Wang.

Hybrid high-order methods for elliptic PDEs on curved and complicated domains. Spectral and High Order Methods for Partial Differential Equations ICOSAHOM 2020+1 (2023). (Hal Link)

Chapters in peer-reviewed volumes

1. P. F. Antonietti, A. Cangiani, J Collis, Z. Dong, E. H. Georgoulis, S. Giani, and P. Houston.  

Review of discontinuous Galerkin finite element methods for partial differential equations on complicated domains.  In Building Bridges: Connections and Challenges in Modern Approaches to Numerical Partial Differential Equations. Lecture Notes in Computational Science and Engineering, Springer (2016).

Other publications

1.  Z. Dong, E. H. Georgoulis, J. Levesley, and F. Usta.

Fast multilevel sparse Gaussian kernels for high-dimensional approximation and integration. arXiv preprint arXiv:1501.03296 (2015).

2. Z. Dong.

Discontinuous Galerkin Methods on Polytopic Meshes. D.Phil. Thesis, Department of Mathematics, University of Leicester (2016). (Thesis Link)