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Hailiang Liu



CAM Seminar



  • H. Liu and P. Markowich
    Selection dynamics for deep neural networks (arXiv:1905.09076 )
  • H. Yu and H. Liu
    Third order maximum-principle-satisfying DG schemes for convection-diffusion problems with anisotropic diffusivity 
    Journal Comp. Physics. 391: 14–36, 2019.
  • H. Liu, R. Groepler, and G. Warnecke 
    A high order positivity preserving DG method for coagulation-fragmentation equations
    SIAM J. Sci. Comput., 41(3): B448--B465, 2019.
  • H. Liu and P-M. Yin 
    A mixed discontinuous Galerkin method without interior penalty for time-dependent fourth order problems
    J. of Scientific Computing. 77(1), 467--501, 2018.
  • Yi Jiang and H. Liu
    Invariant-region-preserving DG methods for multi-dimensional hyperbolic conservation law systems, with an application to compressible Euler equations,
    Journal of Comput. Phys. 373(15), 385--409, 2018.
  • P-E. Jabin and H. Liu
    On a nonlocal selection-mutation model with a gradient flow structure, Nonlinearity, 30:4220--4238, 2017.
  • H. Liu and Z.-M. Wang
    A free energy satisfying discontinuous Galerkin method for Poisson-Nernst-Planck systems, J. Comput. Phys. 238: 413--437, 2017.
  • T. Li, H. Liu and L.-H. Wang
    On traveling wave solutions to the Keller-Segel model of mixed type, J. Differential Equations, 261: 7080--7098, 2016.
  • H. Liu, O. Runborg and N. Tanushev
    Sobolev and Max Norm Error Estimates for Gaussian Beam Superpositions, Comm. Math. Sci. 14(7): 2041--2076, 2016.
  • D. Levermore, H. Liu and R. Pego
    Global dynamics of Bose-Einstein condensation for a model of the Kompaneets equation, SIAM J. MATH. ANAL. 48(4): 2454--2494, 2016.
  • H. Liu and Z.-M. Wang
    An entropy satisfying discontinuous Galerkin method for nonlinear Fokker-Planck equations J Sci Comput., 68:1217--1240, 2016.
  • H. Liu and N.-Y. Yi,
    A Hamiltonian preserving discontinuous Galerkin method for the generalized Korteweg-de Vries equation, J. Comp. Phys, 15: 776--796, 2016.
  • H. Liu and M. Pollack,
    Alternating evolution Galerkin methods for convection-diffusion equations, J. Comp. Phys. 307 (2016), 574--592.

  • Y. Lee and H. Liu
    Threshold for shock formation in the hyperbolic Keller--Segel model, Appl. Math. Letters. 50 (2015), 56--63.
  • H. Liu, W.-L. Cai and N. Su
    Entropy satisfying schemes for computing selection dynamics in competitive interactions, SIAM J. Numer. Anal. 53(3) (2015), 1393--1417.
  • H. Liu
    Optimal error estimates of the directdiscontinuous Galerkin method for convection-diffusion equations,  Math. Comp. 84 (2015), 2263--2295.
  • H. Liu and M. Pryporov
    Error estimates of the Bloch band-based Gaussian beam superposition for the Schroedinger equation, Contemporary math. 640 (2015), 87--114.

  • H. Liu and H. Yu,
    Maximum-principle-satisfying third order discontinuous Galerkin schemes for Fokker-Planck equations, SIAM J. Sci. Comput. 36(5)(2014), A2296--A2325.
  • H. Liu,J. Ralston, O. Runborg and N. Tanushev
    Gaussian beam methods for the Helmholtz equation, SIAM J. Appl. Math. 74(3) (2014), 771--793.
  • H. Liu and M. Pollack
    Alternating evolution DG methods for Hamilton-Jacobi equations, J. Comput. Phys. 258 (2014), 32-46.
  • H. Liu and Hui Yu
    Entropy/Energy stable schemes for evolutionary dispersal models,  J. Comp. Phys. 256 (2014),656--677.
  • Yongki Lee and H. Liu
    Thresholds in three-dimensional restricted Euler-Poisson equations, Phys. D. 262 (2013), 59--70.
  • H. Liu, O. Runborg and N. Tanushev
    Error estimates for Gaussian beam superpositions, Math Comp. 82 (2013), 919--952.
  • H. Liu and Hui Yu
    An entropy satisfying conservative method for the Fokker Planck equation of FENE dumbbell model. SIAM Journal on Numerical Analysis. 2012, Vol. 50, No. 3, pp. 1207-1239.
  • Jaemin Shin and H. Liu
    Global well-posedness for the microscopic FENE model with a sharp boundary condition, Journal Diff. Equ. 252 (2012), 641--662.
  • Haseena Saran and H. Liu
    Alternating evolution (AE) schemes for hyperbolic conservation laws, SIAM J. on Scientific Computing. 33(6) (2011), 3210--3240.
  • H. Liu and J. Yan
    The Direct Discontinuous Galerkin (DDG) method for diffusion with interface corrections , Commun Comput. Phys. 8(3) (2010), 541--564.
  • H. Liu and J. Ralston
    Recovery of high frequency wave fields from phase space based measurements, Multiscale Model. Simul. 8(2) (2010), 622--644.