Preprints and Technical Reports
- Q. Chen, Z. Sun and Y. Xing, The Runge—Kutta discontinuous Galerkin method with stage-dependent polynomial spaces for hyperbolic conservation laws, arXiv:2402.15150, preprint.
- M. Peng, Z. Sun and K. Wu, OEDG: Oscillation-eliminating discontinuous Galerkin method for hyperbolic conservation laws, arXiv:2310.04807, submitted for publication.
- 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.
- 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
- 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.
- 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 Compuation, v6 (2024), pp.658-687.
- 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. [Accepted Manuscript]
- J. Gopalakrishnan and Z. Sun, Stability of structure-aware Taylor methods for tents, Mathematics of Computation, v92 (2023), pp.1061-1086.
- 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.
- Z. Sun and C.-W. Shu, Enforcing stability of explicit Runge—Kutta methods with superviscosity, Communications on Applied Mathematics and Computation, v3 (2021), pp.671-700.
- 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.
- 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.
- 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.
- 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.
- Z. Sun and C.-W. Shu, Strong stability of explicit Runge—Kutta time discretizations, SIAM Journal on Numerical Analysis, v57 (2019), pp.1158-1182.
- 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.
- 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.
- 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.
- 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.