- Design and analysis of discontinuous
Galerkin finite element methods.
- Design simple and compact WENO
limiters for discontinuous Galerkin methods.
- Deterministic numerical
simulations of kinetic transport, with applications in plasma physics.
- High order computational methods,
including finite difference and finite volume WENO methods, spectral
methods.
- Uncertainty quantification and
stochastic computations.

1. X. Zhong and
C.-W. Shu__, ____Numerical resolution of discontinuous
Galerkin methods for time dependent wave equations__, Computer Methods in
Applied Mechanics and Engineering, v200 (2011), pp. 2814-2827.

2. X. Zhong and
C.-W. Shu, __A simple
weighted essentially nonoscillatory limiter for Runge-Kutta discontinuous
Galerkin methods__, Journal of Computational Physics, v232 (2012), pp.
397-415.

3. W. Guo, X. Zhong and J.-M. Qiu,
__Superconvergence
of discontinuous Galerkin method: eigen-structures analysis based on Fourier
approach__, Journal of Computational Physics, v235 (2013), pp. 458-485.

4. J. Zhu, X. Zhong, C.-W. Shu and J.X. Qiu, __Runge-Kutta
discontinuous Galerkin method using a new type of WENO limiters on unstructured
meshes__, Journal of Computational
Physics, v248 (2013), pp. 200-220.

5. Y. Cheng, A. J. Christlieb and X. Zhong*,
__Energy-conserving
discontinuous Galerkin methods for the Vlasov-Ampére system,__ Journal
of Computational Physics, v256 (2014), pp. 630-655.

6. Y. Cheng, A. J. Christlieb and X. Zhong*, __Energy-conserving
discontinuous Galerkin methods for the Vlasov-Maxwell system__, Journal
of Computational Physics, v279 (2014), pp. 145-173.

7. Y. Cheng, A. J. Christlieb and X. Zhong, __Energy-conserving
numerical simulations of electron holes in two-species plasmas__,
European Physical Journal D, v69 (2015), pp. 1-19.

8. Y. Cheng, A. J. Christlieb and X. Zhong*, __Numerical study of the two-species
Vlasov-Ampére system: energy-conserving schemes and the current-driven
ion-acoustic instability__, Journal of
Computational Physics, v288 (2015), pp. 66-85.

9. W. Guo, R. D. Nair, X. Zhong*, __An efficient
WENO limiter for discontinuous Galerkin transport scheme on the cubed sphere__,
International Journal for Numerical Methods in Fluids, v81
(2016), pp. 3-21.

10. J. Zhu, X. Zhong, C.-W. Shu and J.X. Qiu, __Runge-Kutta
discontinuous Galerkin method with a simple and compact Hermite WENO limiter__,
Communications in Computational Physics, v19
(2016), pp. 944-969.

11.J. Zhu, X. Zhong, C.-W. Shu and J.X. Qiu, __Runge-Kutta
discontinuous Galerkin method with a simple and compact Hermite WENO limiter on
unstructured meshes__, Communications in
Computational Physics, v21 (2017), pp 623-649.

12.X.
Zhong and Q. Li, Galerkin
Method for Stationary Radiative Transfer Equations
with Uncertain Coefficients, Journal of Scientific Computing, to appear.

13.T. Chen, N. Gewecke, Z. Li, A.C. Rubiano, R. Shuttleworth, B. Yang and X. Zhong,
__Fast
Computational Methods for Reservoir Flow Models__, IMA Preprint Series
2286 (2009).