Hailiang  Liu
Cited by
Cited by
Formation of δ-shocks and vacuum states in the vanishing pressure limit of solutions to the Euler equations for isentropic fluids
GQ Chen, H Liu
SIAM journal on mathematical analysis 34 (4), 925-938, 2003
The direct discontinuous Galerkin (DDG) methods for diffusion problems
H Liu, J Yan
SIAM Journal on Numerical Analysis 47 (1), 675-698, 2009
Concentration and cavitation in the vanishing pressure limit of solutions to the Euler equations for nonisentropic fluids
GQ Chen, H Liu
Physica D: Nonlinear Phenomena 189 (1-2), 141-165, 2004
Critical thresholds in Euler-Poisson equations
S Engelberg, H Liu, E Tadmor
Indiana University Mathematics Journal, 109-157, 2001
The direct discontinuous Galerkin (DDG) method for diffusion with interface corrections
H Liu, J Yan
Communications in Computational Physics 8 (3), 541, 2010
Critical thresholds in a convolution model for nonlinear conservation laws
H Liu, E Tadmor
SIAM Journal on Mathematical Analysis 33 (4), 930-945, 2001
Axial symmetry and classification of stationary solutions of Doi-Onsager equation on the sphere with Maier-Saupe potential
H Liu, H Zhang, P Zhang
Communications in Mathematical Sciences 3 (2), 201-218, 2005
Spectral Dynamics of the Velocity Gradient Field¶ in Restricted Flows
H Liu, E Tadmor
Communications in Mathematical Physics 228 (3), 435-466, 2002
Computing multivalued physical observables for the semiclassical limit of the Schrödinger equation
S Jin, H Liu, S Osher, YHR Tsai
Journal of Computational Physics 205 (1), 222-241, 2005
Critical thresholds in 2D restricted Euler-Poisson equations
E Tadmor, H Liu
SIAM Journal on Applied Mathematics 63 (6), 1889-1910, 2003
Rotation prevents finite-time breakdown
H Liu, E Tadmor
Physica D: Nonlinear Phenomena 188 (3-4), 262-276, 2004
Computational high-frequency wave propogation using the level-set method with applications to the semi-classical limit of the Schrödinger equations
LT Cheng, H Liu, S Osher
Communications in Mathematical Sciences 1 (3), 593-621, 2003
Error estimates for Gaussian beam superpositions
H Liu, O Runborg, N Tanushev
MATHEMATICS OF COMPUTATION 82 (282), 919--952, 2013
A local discontinuous Galerkin method for the Korteweg–de Vries equation with boundary effect
H Liu, J Yan
Journal of Computational Physics 215 (1), 197-218, 2006
A free energy satisfying finite difference method for Poisson–Nernst–Planck equations
H Liu, Z Wang
Journal of Computational Physics 268, 363-376, 2014
Optimal error estimates of the direct discontinuous Galerkin method for convection-diffusion equations
H Liu
Mathematics of computation 84 (295), 2263-2295, 2015
Computing multi-valued physical observables for the high frequency limit of symmetric hyperbolic systems
S Jin, H Liu, S Osher, R Tsai
Journal of Computational Physics 210 (2), 497-518, 2005
Kinetic models for polymers with inertial effects
P Degond, H Liu
arXiv preprint arXiv:0901.1909, 2009
Convergence rates for relaxation schemes approximating conservation laws
H Liu, G Warnecke
SIAM journal on numerical analysis 37 (4), 1316-1337, 2000
Recovery of high frequency wave fields from phase space–based measurements
H Liu, J Ralston
Multiscale Modeling & Simulation 8 (2), 622-644, 2010
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