Publications

Publications in Refereed Journals (Appeared or Accepted)

  1. Y. Liu, C.-W. Shu and M. Zhang, Entropy stable high order discontinuous Galerkin methods for ideal compressible MHD on structured meshes , Journal of Computational Physics, v354 (2018), pp. 163-178.

  2. Y. Liu, C.-W. Shu and M. Zhang, Optimal error estimates of the semidiscrete central discontinuous Galerkin methods for linear hyperbolic equations , SIAM Journal on Numerical Analysis, v56 (2018), pp. 520-541.

  3. Y. Liu, C.-W. Shu and M. Zhang, Superconvergence of energy-conserving discontinuous Galerkin methods for linear hyperbolic equations , Communications on Applied Mathematics and Computation, v1 (2019), pp.101-116.

  4. Y. Liu, Q. Liu, Y. Liu, C.-W. Shu and M. Zhang, Locally divergence-free spectral-DG methods for ideal magnetohydrodynamic equations on cylindrical coordinates , Communications in Computational Physics, v26 (2019), pp. 631-653.

  5. Y. Liu, T. Chen, Y. Chen and C.-W. Shu, Certified offline-free reduced basis (COFRB) methods for stochastic differential equations driven by arbitrary types of noise , Journal of Scientific Computing, v81 (2019), pp. 1210-1239.

  6. Y. Liu, C.-W. Shu and M. Zhang, Optimal error estimates of the semidiscrete discontinuous Galerkin methods for two dimensional hyperbolic equations on Cartesian meshes using $P^k$ elements , ESAIM: Mathematical Modelling and Numerical Analysis ($M^{2}AN$), v54 (2020), pp.705-726.

  7. M. Jiao, Y. Cheng, Y. Liu and M. Zhang, Central discontinuous Galerkin methods for the generalized Korteweg-de Vires equation, Communications in Computational Physics, to appear.

  8. A. Chen, Y. Cheng, Y. Liu and M. Zhang, Superconvergence of ultra-weak discontinuous Galerkin methods for the linear Schrödinger equation in one dimension , Journal of Scientific Computing, v82 (2020), article number 22.

  9. Y. Liu, C.-W. Shu, and M. Zhang, Sub-optimal convergence of discontinuous Galerkin methods with central fluxes for linear hyperbolic equations with even degree polynomial approximations , Journal of Computational Mathematics, to appear.

  10. Y. Liu, Q. Tao, and C.-W. Shu, Analysis of optimal superconvergence of an ultraweak-local discontinuous Galerkin method for a time dependent fourth-order equation , ESAIM: Mathematical Modelling and Numerical Analysis ($M^{2}AN$), v54 (2020), pp.1797-1820.



Preprints

  1. Y. Liu, J. Lu, C.-W. Shu, and M. Zhang, Central discontinuous Galerkin methods on overlapping meshes for wave equations, submitted to ESAIM: Mathematical Modelling and Numerical Analysis ($M^{2}AN$).

  2. J. Lu, Y. Liu, and C.-W. Shu, An oscillation-free discontinuous Galerkin method for scalar hyperbolic conservation laws , submitted to SIAM Journal on Numerical Analysis.