Publications in Refereed Journals (Appeared or Accepted)

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. 163178.

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. 520541.

Y. Liu, C.W. Shu, and M. Zhang,
Superconvergence of energyconserving discontinuous Galerkin methods for linear hyperbolic equations
(Focused Issue in memory of Professor Benyu Guo),
Communications on Applied Mathematics and Computation, v1 (2019), pp.101116.

Y. Liu, Q. Liu, Y. Liu, C.W. Shu, and M. Zhang,
Locally divergencefree spectralDG methods for ideal magnetohydrodynamic equations on cylindrical coordinates
,
Communications in Computational Physics, v26 (2019), pp. 631653.

Y. Liu, T. Chen, Y. Chen, and C.W. Shu,
Certified offlinefree 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. 12101239.

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.705726.

M. Jiao, Y. Cheng, Y. Liu and M. Zhang,
Central discontinuous Galerkin methods for the generalized Kortewegde Vires equation
, Communications in Computational Physics, v28(2020), pp. 927966.

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

Y. Liu, Q. Tao, and C.W. Shu,
Analysis of optimal superconvergence of an ultraweaklocal discontinuous Galerkin method for a time dependent fourthorder equation
,
ESAIM: Mathematical Modelling and Numerical Analysis ($M^{2}AN$), v54 (2020), pp.17971820.

Y. Liu, C.W. Shu, and M. Zhang,
Suboptimal convergence of discontinuous Galerkin methods with central fluxes for linear hyperbolic equations with even degree polynomial approximations
,
Journal of Computational Mathematics, v39(2021), pp. 629648.

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.329356.

J. Lu, Y. Liu, and C.W. Shu,
An oscillationfree discontinuous Galerkin method for scalar hyperbolic conservation laws
,
SIAM Journal on Numerical Analysis, v59 (2021), pp. 12991324.

Y. Liu, J. Lu, and C.W. Shu,
An essentially oscillationfree discontinuous Galerkin method for hyperbolic systems
, SIAM Journal on Scientific Computing, v44 (2022), pp. A230A259.

J. Huang, Y. Liu, Y. Liu, Z. Tao, and Y. Cheng,
A class of adaptive multiresolution ultraweak discontinuous Galerkin methods for some nonlinear dispersive wave equations
, SIAM Journal on Scientific Computing, v44 (2022), pp. A745A769.

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

Q. Tao, Y. Liu, Y. Jiang, and J. Lu,
An oscillationfree local discontinuous Galerkin method for nonlinear degenerate parabolic equations
, Numerical Methods for Partial Differential Equations, v39 (2023), pp. 31453169.

J. Du, Y. Liu, and Y. Yang,
An oscillationfree boundpreserving discontinuous Galerkin method for multicomponent chemically reacting flows
, Journal of Scientific Computing, v95 (2023), article number 90.

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.

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. 118.

Y. Liu, J. Lu, and C.W. Shu,
An entropy stable essentially oscillationfree disontinuous Galerkin method for hyperbolic conservation laws
, SIAM Journal on Scientific Computing, to appear.
Preprints

Z. Chen, Y. Liu, and X. Xiang,
A high order explicit time finite element method for the acoustic wave equation with discontinuous coefficients
, submitted.

Z. Chen and Y. Liu,
Efficient and Parallel Solution of Highorder Continuous Time Galerkin for Dissipative and Wave Propagation Problems
, submitted.

Q. Tao, X. Chang, Y. Liu and C.W. Shu,
A local discontinuous Galerkin method for the Novikov equation
, submitted.