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 (Focused Issue in memory of Professor Ben-yu Guo), 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 (a special section in memory of Professor Saul Abarbanel), 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, v28(2020), pp. 927-966.

  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, 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.

  10. 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, v39(2021), pp. 629-648.

  11. Y. Liu, J. Lu, C.-W. Shu, and M. Zhang, Central discontinuous Galerkin methods on overlapping meshes for wave equations , ESAIM: Mathematical Modelling and Numerical Analysis ($M^{2}AN$), v55 (2021), pp.329-356.

  12. J. Lu, Y. Liu, and C.-W. Shu, An oscillation-free discontinuous Galerkin method for scalar hyperbolic conservation laws , SIAM Journal on Numerical Analysis, v59 (2021), pp. 1299-1324.

  13. Y. Liu, J. Lu, and C.-W. Shu, An essentially oscillation-free discontinuous Galerkin method for hyperbolic systems , SIAM Journal on Scientific Computing, v44 (2022), pp. A230-A259.

  14. J. Huang, Y. Liu, Y. Liu, Z. Tao, and Y. Cheng, A class of adaptive multiresolution ultra-weak discontinuous Galerkin methods for some nonlinear dispersive wave equations , SIAM Journal on Scientific Computing, v44 (2022), pp. A745-A769.

  15. Y. Liu, J. Lu, Q. Tao, and Y. Xia, An oscillation-free discontinuous Galerkin method for shallow water equations , Journal of Scientific Computing, v92 (2022), article number 109.

  16. Q. Tao, Y. Liu, Y. Jiang, and J. Lu, An oscillation-free local discontinuous Galerkin method for nonlinear degenerate parabolic equations , Numerical Methods for Partial Differential Equations, v39 (2023), pp. 3145-3169.

  17. J. Du, Y. Liu, and Y. Yang, An oscillation-free bound-preserving discontinuous Galerkin method for multi-component chemically reacting flows , Journal of Scientific Computing, v95 (2023), article number 90.

  18. Z. Chen and Y. Liu, An Arbitrarily High Order Unfitted Finite Element Method for Elliptic Interface Problems with Automatic Mesh Generation , Journal of Computational Physics, v491(2023), 112384.

  19. Z. Chen and Y. Liu, An arbitrarily high order finite element method on arbitrarily shaped domains with automatic mesh generation (in Chinese, Dedicated to 90th Birthday of Prof. Lishang Jiang), SCIENTIA SINICA Mathematica, v54 (2024), pp. 337-354.

  20. Y. Liu, J. Lu, and C.-W. Shu, An entropy stable essentially oscillation-free disontinuous Galerkin method for hyperbolic conservation laws , SIAM Journal on Scientific Computing, v46(2024), pp. A1132-A1159.

  21. Z. Chen and Y. Liu, Efficient and Parallel Solution of High-order Continuous Time Galerkin for Dissipative and Wave Propagation Problems , SIAM Journal on Scientific Computing, v46(2024), pp. A2073-A2100.

  22. Z. Chen and Y. Liu, An arbitrarily high order unfitted finite element method for elliptic interface problems with automatic mesh generation, Part II. Piecewise-smooth interfaces , Applied Numerical Mathematics, v206(2024), pp. 247-268.

  23. Q. Tao, X.-K. Chang, Y. Liu, and C.-W. Shu, A local discontinuous Galerkin method for the Novikov equation , Mathematics of Computation, to appear.

  24. Z. Chen, Y. Liu, and X. Xiang, A high order explicit time finite element method for the acoustic wave equation with discontinuous coefficients , CSIAM Transactions on Applied Mathematics, v5(2024), pp. 735 - 787.

Preprints

  1. Y. Liu and Z. Xu, An Interior Penalty Discontinuous Galerkin Method for an Interface Model of Flow in Fractured Porous Media , preprint

  2. Y. Liu, J. Lu, and C.-W. Shu, An entropy stable essentially oscillation-free discontinuous Galerkin method for solving ideal magnetohydrodynamic equations , submitted to Journal of Computational Physics.