Preprints and Technical Reports

  1. Z. Xu, Z. Sun and Y.-T. Zhang, Stability and time-step constraints of exponential time differencing Runge–Kutta discontinuous Galerkin methods for advection-diffusion equations,  arXiv:2503.03019,  submitted for publication.
  2. Z. Sun and Y. Xing,  On a numerical artifact of solving shallow water equations with a discontinuous bottom: Analysis and a nontransonic fix,  arXiv:2308.09265,  preprint.
  3. Z. Sun and C.-W. Shu, Error analysis of Runge–Kutta discontinuous Galerkin methods for linear time-dependent partial differential equations.​ arXiv:2001.00971.

Accepted or Appeared in Refereed Journals

  1. C. Liu, Z. Sun and X. Zhang,  A bound-preserving Runge–Kutta discontinuous Galerkin method with compact stencils for hyperbolic conservation laws, Journal of Computational Physics, Volume 537 (2025), 114071.
  2. Q. Chen, Z. Sun and Y. Xing,  The Runge–Kutta discontinuous Galerkin method with stage-dependent polynomial spaces for hyperbolic conservation laws, Journal of Computational Physics, v523 (2025), 113654.
  3. Z. Sun,  Reducing polynomial degree by one for inner-stage operators affects neither stability type nor accuracy order of the Runge–Kutta discontinuous Galerkin method,  arXiv:2404.15453v2, Mathematics of Computation, to appear.
  4. M. Peng, Z. Sun and K. Wu, OEDG: Oscillation-eliminating discontinuous Galerkin method for hyperbolic conservation laws, Mathematics of Computation, 94 (2025), 1147-1198.
  5. Q. Chen, Z. Sun and Y. Xing, The Runge–Kutta discontinuous Galerkin method with compact stencils for hyperbolic conservation laws, SIAM Journal on Scientific Computing, v46 (2024), pp.A1327-A1351.
  6. J. Hunter, Z. Sun and Y. Xing, Stability and time-step constraints of implicit-explicit Runge–Kutta methods for the linearized Korteweg–de Vries equation, Communications on Applied Mathematics and Computation, v6 (2024), pp.658-687.
  7. Z. Sun and Y. Xing, On generalized Gauss–Radau projections and optimal error estimates of upwind-biased DG methods for the linear advection equation on special simplex meshes, Journal of Scientific Computing, v95 (2023), 40. 
  8. J. Gopalakrishnan and Z. Sun,​ Stability of structure-aware Taylor methods for tents, Mathematics of Computation, v92 (2023), pp.1061-1086.
  9. Z. Sun, Y. Wei and K. Wu, ​ On energy laws and stability of Runge–Kutta methods for linear seminegative problems, SIAM Journal on Numerical Analysis, v60 (2022), pp.2448-2481.
  10. Z. Sun and C.-W. Shu, Enforcing strong stability of explicit Runge–Kutta methods with superviscosity, Communications on Applied Mathematics and Computation, v3 (2021), pp.671-700.
  11. Z. Sun, S. Wang, L.-B. Chang, Y. Xing and D. Xiu, Convolution neural network shock detector for numerical solution of conservation laws, Communications in Computational Physics, v28 (2020), pp. 2075-2108.
  12. Z. Sun and Y. Xing, Optimal error estimates of discontinuous Galerkin methods with generalized fluxes for wave equations on unstructured meshes, Mathematics of Computation, v90 (2021), pp.1741-1772. 
  13. Z. Sun and Y. Xing, On structure-preserving discontinuous Galerkin methods for Hamiltonian partial differential equations: Energy conservation and multi-symplecticity, Journal of Computational Physics, v419 (2020), 109662. 
  14. Z. Sun and C.D. Hauck, Low-memory, discrete ordinates, discontinuous Galerkin methods for radiative transport, SIAM Journal on Scientific Computing, v42 (2020), pp.B869-B893. 
  15. Z. Sun and C.-W. Shu, Strong stability of explicit Runge—Kutta time discretizations, SIAM Journal on Numerical Analysis, v57 (2019), pp.1158-1182. 
  16. Z. Sun, J.A. Carrillo and C.-W. Shu, An entropy stable high-order discontinuous Galerkin method for cross-diffusion gradient flow systems, Kinetic and Related Models, v12 (2019), pp.885-908. 
  17. Z. Sun, J.A. Carrillo and C.-W. Shu, A discontinuous Galerkin method for nonlinear parabolic equations and gradient flow problems with interaction potentials, Journal of Computational Physics, v352 (2018), pp.76-104. 
  18. Z. Sun and C.-W. Shu, Stability of the fourth order Runge–Kutta method for time-dependent partial differential equations, Annals of Mathematical Sciences and Applications, v2 (2017), pp.255-284.
  19. Z. Sun and C.-W. Shu, Stability analysis and error estimates of Lax–Wendroff discontinuous Galerkin methods for linear conservation laws, ESAIM: Mathematical Modelling and Numerical Analysis, v51 (2017), pp.1063-1087.