Publications

Recent preprints

1.  Z. Dong, Z. Wang and L. Zhao,

Pressure-robust hp-a posteriori error estimates of 𝐻(div) -conforming discontinuous Galerkin methods for the Stokes equations. Submitted for publication. (ArXiv Link) (HaL Link)

2.  Z. Dong and E. H. Georgoulis,

Hypocoercivity-preserving space-time Galerkin methods for kinetic Fokker-Planck equations. Submitted for publication. (ArXiv Link) (HaL Link)

3.  Z. Dong, C. Maradei and M. Vohraílk.

Approximate inexpensive multigrid block-Jacobi solver using extension of basis functions and a levelwise optimal step-size. Submitted for publication. (HaL Link)

4.  T. Chaumont-Frelet, Z. Dong, G. Gantner and M. Vohraílk.

On p-robust convergence and optimality of adaptive FEM driven by equilibrated-flux estimators. Submitted for publication. (ArXiv Link) (HaL Link)

5.  Z. Dong, T. Huang and B. Li.

Weighted H^2 regularity of fluid-structure interaction when the interface intersects the boundary. Submitted for publication. (HaL Link)

6.  Z. Dong, A. Ern and T. Wadhawan.

hp-a posteriori error estimates for hybrid high-order methods applied to biharmonic problems. Submitted for publication. (ArXiv Link) (HaL Link)

7.  Z. Dong and T. Wadhawan.

On the constants in inverse trace inequalities for polynomials orthogonal to lower-order subspaces. Submitted for publication. (ArXiv Link) (HaL Link)

8.  J. Zhao, W. Zhu, Z. Dong and S. Mao.

The pressure-robust virtual element methods with reconstruction for the Stokes equation. Submitted for publication. (HaL Link)

Articles in peer-reviewed journals​

1.  Z. Dong, E. H. Georgoulis, L. Mascotto and Z. Wang.

A posteriori error analysis and adaptivity of a space-time finite element method for the wave equation in second order formulation. Accepted in Numerische Mathematik. (ArXiv Link) (Hal Link)

2.  Z. Dong and A. Ern.

hp-error analysis of mixed-order hybrid high-order methods for elliptic problems on simplicial meshes. Accepted in Numerische Mathematik. (ArXiv Link) (Hal Link)

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

Asymptotic numerical hypocoercivity of the space-time discontinuous Galerkin method for Kolmogorov equation. Accepted in Mathematics of Computation. (ArXiv Link) (Hal Link)

4.  Z. Dong, L. Mascotto and Z. Wang.

A priori and a posteriori error estimates of a C^0-in-time method for the wave equation in second order formulation. Accepted in Numerische Mathematik. (ArXiv Link) (Hal Link)

5.  Z. Dong and A. Ern.

𝐻(𝐜𝐮𝐫𝐥)-reconstruction of piecewise polynomial fields with application to hp-a posteriori nonconforming error analysis for Maxwell's equations. Accepted in SIAM Journal on Numerical Analysis. (ArXiv Link) (Hal Link)

6.  M. Zhang, Z. Dong and W. Yan.

hp-version discontinuous Galerkin time-stepping schemes for diffusive-viscous wave equation. Computers & Mathematics with Applications, 200, 145-166 (2025) (Hal Link)

7.  Z. Dong, A. Ern and Z. Wang.

A bound-preserving scheme for the Allen-Cahn equation. Computers & Mathematics with Applications, 199, 225-241 (2025) (Hal Link)

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

Homogeneous multigrid for hybrid discretizations: application to HHO methods. Numerical Methods for Partial Differential Equations, 41(5), (ArXiv Link) (Hal Link)

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

A hypocoercivity-exploiting stabilised finite element method for Kolmogorov equation. SIAM Journal on Numerical Analysis, 64(3), 1105–1127 (2025). (ArXiv Link) (Hal Link)

10.  Z. Dong and L. Mascotto.

hp-optimal convergence of the original DG method for linear hyperbolic problems on special simplicial meshes. IMA Journal of Numerical Analysis, 45 (3),pp.1372–1396. (ArXiv Link) (Hal Link)

11.  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)

12.  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)

13.  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)

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, 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)

16.  Z. Dong and E. H. Georgoulis.

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

17.  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)

18.   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)

19.  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)

20.  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)

21.  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)

22.  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) 

23.  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)

24.  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)

25.  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).

26.  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)

27.  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)