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
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Journal of Computational Physics , v354 (2018), pp. 163-178.
Y. Liu, C.-W. Shu and M. Zhang,
Optimal error estimates of the semidiscrete central discontinuous Galerkin methods for linear hyperbolic equations
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SIAM Journal on Numerical Analysis , v56 (2018), pp. 520-541.
Y. Liu, C.-W. Shu and M. Zhang,
Superconvergence of energy-conserving discontinuous Galerkin methods for linear hyperbolic equations
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Communications on Applied Mathematics and Computation , v1 (2019), pp.101-116.
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
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Communications in Computational Physics , v26 (2019), pp. 631-653.
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
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Journal of Scientific Computing , v81 (2019), pp. 1210-1239.
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
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ESAIM: Mathematical Modelling and Numerical Analysis ($M^{2}AN$) , v54 (2020), pp.705-726.
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.
A. Chen, Y. Cheng, Y. Liu and M. Zhang,
Superconvergence of ultra-weak discontinuous Galerkin methods for the linear Schrödinger equation in one dimension
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Journal of Scientific Computing , v82 (2020), article number 22.
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
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Journal of Computational Mathematics , to appear.
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
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ESAIM: Mathematical Modelling and Numerical Analysis ($M^{2}AN$) , v54 (2020), pp.1797-1820.
Preprints
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 ($M^{2}AN$) .
J. Lu, Y. Liu, and C.-W. Shu,
An oscillation-free discontinuous Galerkin method for scalar hyperbolic conservation laws
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submitted to SIAM Journal on Numerical Analysis .