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Author ID: liu.hailiang Recent zbMATH articles by "Liu, Hailiang"
Published as: Liu, Hailiang; Liu, H.; Liu, Hai-liang
all top 5

Co-Authors

23 single-authored
9 Wang, Jinghua
9 Wang, Zhongming
8 Huang, Yunqing
8 Tadmor, Eitan
8 Yi, Nianyu
8 Yin, Peimeng
6 Warnecke, Gerald G.
6 Yu, Hui
5 Bhatnagar, Manas
5 Cai, Wenli
5 Li, Tong
5 Osher, Stanley Joel
4 Jiang, Yi
4 Jin, Shi
4 Ralston, James V.
4 Yang, Tong
3 Jabin, Pierre-Emmanuel
3 Lee, Yongki
3 Maimaitiyiming, Wumaier
3 Pollack, Michael
3 Runborg, Olof
3 Shin, Jaemin
3 Tanushev, Nicolay M.
3 Tsai, Yen-Hsi Richard
3 Yan, Jue
2 Bernussou, Jacques
2 Chen, Gui-Qiang G.
2 Cheng, Li-Tien
2 Degond, Pierre
2 Hadji, Layachi
2 Himeno, Ryutaro
2 Krishnan, Sreedevi
2 Lu, Wenying
2 Marella, Saikrishna V.
2 Pan, Jun
2 Pryporov, Maksym
2 Saran, Haseena
2 Schreiber, Willard C.
2 Shyy, Wei
2 Udaykumar, Holavanahalli S.
2 Wen, Hairui
2 Yamaguchi, Takami
1 Akulichev, Victor A.
1 Aten, Charlotte
1 Ates, Muzaffer
1 Axhausen, Kay W.
1 Ayachi, B.
1 Bajcinca, Naim
1 Barthès-Biesel, Dominique
1 Bathe, Klaus-Jürgen
1 Bau, E.
1 Bazargan-Sabet, B.
1 Borhan, Ali
1 Bressan, Alberto
1 Butterfaß, J.
1 Cao, Waixiang
1 Cesnik, Carlos E. S.
1 Chanchole, S.
1 Chui, E.
1 Cleary, Michael P.
1 Davulcu, Hasan
1 Desai, Chandra S.
1 Di Francesco, Marco
1 Dirr, Bodo
1 Engelberg, Shlomo
1 Fan, Haitao
1 Fan, Yuanxun
1 Fellner, Klemens
1 Feng, Xiaobing
1 Fox, Rodney O.
1 Garg, Hari Krishna
1 Gröpler, Robin
1 Gupta, N. R.
1 Ha, Tae Gab
1 Huang, Yuxia
1 Huo, Xiaokai
1 Ifju, Peter G.
1 Ikehata, Masaru
1 Iosevich, Alex
1 Jackiewicz, Zdzislaw
1 Katz, Casimir
1 Knoch, S.
1 Kobayashi, Shoichi
1 Kolippakkam, D.
1 Kuang, Yang
1 Lebon, Frédéric
1 Levermore, C. David
1 Li, Bingtuan
1 Lian, Yongsheng
1 Liang, Fugang
1 Liao, Guojun
1 Lien, Fue-Sang
1 Liu, Chun
1 Lott, Adam
1 Ma, Shu
1 MacKinnon, I.
1 Maimon, Shir
1 Markowich, Peter Alexander
1 McCartney, C. J.
1 Mehl, Michael J.
...and 58 more Co-Authors
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Serials

24 Journal of Computational Physics
8 Mathematics of Computation
8 Journal of Differential Equations
8 Journal of Scientific Computing
8 Communications in Computational Physics
6 SIAM Journal on Numerical Analysis
6 Physica D
6 Applied Mathematics Letters
6 SIAM Journal on Scientific Computing
6 Communications in Mathematical Sciences
5 SIAM Journal on Mathematical Analysis
4 Journal of Computational and Applied Mathematics
4 M\(^3\)AS. Mathematical Models & Methods in Applied Sciences
4 Discrete and Continuous Dynamical Systems
3 International Journal for Numerical Methods in Fluids
3 International Journal of Solids and Structures
3 Numerische Mathematik
3 Numerical Methods for Partial Differential Equations
3 SIAM Journal on Applied Mathematics
3 Methods and Applications of Analysis
3 Journal of Hyperbolic Differential Equations
2 Computers and Structures
2 Molecular Simulation
2 Indiana University Mathematics Journal
2 Japan Journal of Industrial and Applied Mathematics
2 Proceedings of the Royal Society of Edinburgh. Section A. Mathematics
2 Multiscale Modeling & Simulation
2 European Series in Applied and Industrial Mathematics (ESAIM): Mathematical Modelling and Numerical Analysis
2 Advances and Applications in Fluid Mechanics
1 Communications in Mathematical Physics
1 Computer Methods in Applied Mechanics and Engineering
1 IMA Journal of Numerical Analysis
1 International Journal of Control
1 International Journal of Non-Linear Mechanics
1 International Journal of Systems Science
1 Journal of Fluid Mechanics
1 Journal of Mathematical Analysis and Applications
1 Journal of Sound and Vibration
1 Mathematical Notes
1 Nonlinearity
1 Transport Theory and Statistical Physics
1 Wave Motion
1 ZAMP. Zeitschrift für angewandte Mathematik und Physik
1 Zeitschrift für Angewandte Mathematik und Mechanik (ZAMM)
1 Fuzzy Sets and Systems
1 International Journal for Numerical Methods in Engineering
1 Journal of Functional Analysis
1 Mathematics and Computers in Simulation
1 Mechanics Research Communications
1 Mathematica Numerica Sinica
1 Acta Mathematicae Applicatae Sinica
1 Circuits, Systems, and Signal Processing
1 Acta Mathematica Hungarica
1 Parallel Computing
1 Applied Numerical Mathematics
1 Acta Mathematicae Applicatae Sinica. English Series
1 Annals of Differential Equations
1 Asymptotic Analysis
1 Signal Processing
1 Systems Science and Mathematical Sciences
1 Numerical Algorithms
1 Communications in Partial Differential Equations
1 Communications in Statistics. Simulation and Computation
1 Acta Mathematica Scientia
1 Journal of Partial Differential Equations
1 Advances in Engineering Software
1 Applied Mathematics. Series A (Chinese Edition)
1 Acustica - Acta Acustica
1 Journal of Vibration and Control
1 Wuhan University Journal of Natural Sciences (WUJNS)
1 Mechanism and Machine Theory
1 Flow, Turbulence and Combustion
1 Journal of Nonlinear Mathematical Physics
1 Communications in Information and Systems
1 Quantum Information Processing
1 Journal of Cosmology and Astroparticle Physics
1 Iranian Journal of Fuzzy Systems
1 Acta Mechanica Sinica
1 Networks and Heterogeneous Media
1 Quantum Studies: Mathematics and Foundations

Publications by Year

Citations contained in zbMATH Open

148 Publications have been cited 1,790 times in 806 Documents Cited by Year
Formation of \(\delta\)-shocks and vacuum states in the vanishing pressure limit of solutions to the Euler equations for isentropic fluids. Zbl 1038.35035
Chen, Gui-Qiang; Liu, Hailiang
176
2003
Concentration and cavitation in the vanishing pressure limit of solutions to the Euler equations for nonisentropic fluids. Zbl 1098.76603
Chen, Gui-Qiang; Liu, Hailiang
87
2004
The direct discontinuous Galerkin (DDG) methods for diffusion problems. Zbl 1189.65227
Liu, Hailiang; Yan, Jue
85
2009
Sharp interface Cartesian grid method. I: An easily implemented technique for 3D moving boundary computations. Zbl 1154.76359
Marella, S.; Krishnan, S.; Liu, H.; Udaykumar, H. S.
72
2005
The direct discontinuous Galerkin (DDG) method for diffusion with interface corrections. Zbl 1364.65200
Liu, Hailiang; Yan, Jue
68
2010
Critical thresholds in Euler-Poisson equations. Zbl 0989.35110
Engelberg, Shlomo; Liu, Hailiang; Tadmor, Eitan
56
2001
Critical thresholds in a convolution model for nonlinear conservation laws. Zbl 1002.35085
Liu, Hailiang; Tadmor, Eitan
38
2001
Computational high-frequency wave propagation using the level set method with applications to the semi-classical limit of Schrödinger equations. Zbl 1084.35066
Cheng, Li-Tien; Liu, Hailiang; Osher, Stanley
37
2003
Spectral dynamics of the velocity gradient field in restricted flows. Zbl 1031.76006
Liu, Hailiang; Tadmor, Eitan
37
2002
A numerical study of insect flight. Zbl 0929.76092
Liu, H.; Kawachi, K.
35
1998
Modeling and simulation of capsules and biological cells. Zbl 1026.92002
35
2003
Effect of initial stress on the propagation behavior of Love waves in a layered piezoelectric structure. Zbl 1005.74033
Liu, H.; Wang, Z. K.; Wang, T. J.
35
2001
Sharp interface Cartesian grid method. II: A technique for simulating droplet interactions with surfaces of arbitrary shape. Zbl 1154.76358
Liu, H.; Krishnan, S.; Marella, S.; Udaykumar, H. S.
35
2005
Computing multivalued physical observables for the semiclassical limit of the Schrödinger equation. Zbl 1072.65132
Jin, Shi; Liu, Hailiang; Osher, Stanley; Tsai, Yen-Hsi Richard
35
2005
A free energy satisfying finite difference method for Poisson-Nernst-Planck equations. Zbl 1349.65317
Liu, Hailiang; Wang, Zhongming
33
2014
Optimal error estimates of the direct discontinuous Galerkin method for convection-diffusion equations. Zbl 1331.65141
Liu, Hailiang
30
2015
Critical thresholds in 2D restricted Euler-Poisson equations. Zbl 1073.35187
Liu, Hailiang; Tadmor, Eitan
30
2003
A numerical study of undulatory swimming. Zbl 0958.76099
Liu, H.; Kawachi, K.
29
1999
A local discontinuous Galerkin method for the Korteweg-de Vries equation with boundary effect. Zbl 1092.65083
Liu, Hailiang; Yan, Jue
26
2006
Axial symmetry and classification of stationary solutions of Doi-Onsager equation on the sphere with Maier-Saupe potential. Zbl 1092.76007
Liu, Hailiang; Zhang, Hui; Zhang, Pingwen
26
2005
A direct discontinuous Galerkin method for the generalized Korteweg-de Vries equation: energy conservation and boundary effect. Zbl 1297.65122
Yi, Nianyu; Huang, Yunqing; Liu, Hailiang
25
2013
Rotation prevents finite-time breakdown. Zbl 1098.76643
Liu, Hailiang; Tadmor, Eitan
24
2004
Wave breaking in a class of nonlocal dispersive wave equations. Zbl 1110.35069
Liu, Hailiang
23
2006
Superconvergence of the direct discontinuous Galerkin method for convection-diffusion equations. Zbl 1361.65061
Cao, Waixiang; Liu, Hailiang; Zhang, Zhimin
22
2017
Error estimates for Gaussian beam superpositions. Zbl 1277.35236
Liu, Hailiang; Runborg, Olof; Tanushev, Nicolay M.
21
2013
A free energy satisfying discontinuous Galerkin method for one-dimensional Poisson-Nernst-Planck systems. Zbl 1406.82021
Liu, Hailiang; Wang, Zhongming
20
2017
Mass preserving discontinuous Galerkin methods for Schrödinger equations. Zbl 1352.65358
Lu, Wenying; Huang, Yunqing; Liu, Hailiang
20
2015
Computing multi-valued physical observables for the high frequency limit of symmetric hyperbolic systems. Zbl 1098.65094
Jin, Shi; Liu, Hailiang; Osher, Stanley; Tsai, Richard
20
2005
Maximum-principle-satisfying third order discontinuous Galerkin schemes for Fokker-Planck equations. Zbl 1341.65038
Liu, Hailiang; Yu, Hui
18
2014
A local discontinuous Galerkin method for the Burgers-Poisson equation. Zbl 1339.65177
Liu, Hailiang; Ploymaklam, Nattapol
18
2015
The entropy satisfying discontinuous Galerkin method for Fokker-Planck equations. Zbl 1320.65143
Liu, Hailiang; Yu, Hui
17
2015
A Hamiltonian preserving discontinuous Galerkin method for the generalized Korteweg-de Vries equation. Zbl 1349.65462
Liu, Hailiang; Yi, Nianyu
15
2016
Computational aerodynamics of low Reynolds number plunging, pitching and flexible wings for MAV applications. Zbl 1271.76285
Shyy, W.; Lian, Y.; Tang, J.; Liu, H.; Trizila, P.; Stanford, B.; Bernal, L.; Cesnik, C.; Friedmann, P.; Ifju, P.
15
2008
Entropy-based fuzzy clustering and fuzzy modeling. Zbl 1147.62348
Yao, J.; Dash, M.; Tan, S. T.; Liu, H.
14
2000
Asymptotic stability of relaxation shock profiles for hyperbolic conservation laws. Zbl 1039.35063
Liu, Hailiang
14
2003
An entropy satisfying discontinuous Galerkin method for nonlinear Fokker-Planck equations. Zbl 1354.35158
Liu, Hailiang; Wang, Zhongming
14
2016
Multi-valued solution and level set methods in computational high frequency wave propagation. Zbl 1120.65110
Liu, H.; Osher, S.; Tsai, R.
13
2006
Stability of a relaxation model with a nonconvex flux. Zbl 0961.35017
Liu, Hailiang; Wang, Jinghua; Yang, Tong
12
1998
Recovery of normal derivatives from the piecewise \(L^2\) projection. Zbl 1408.65009
Huang, Yunqing; Liu, Hailiang; Yi, Nianyu
12
2012
Kinetic models for polymers with inertial effects. Zbl 1183.76614
Degond, Pierre; Liu, Hailiang
12
2009
Recovery of high frequency wave fields from phase space-based measurements. Zbl 1221.35031
Liu, Hailiang; Ralston, James
12
2010
Thresholds for shock formation in traffic flow models with Arrhenius look-ahead dynamics. Zbl 1304.35420
Lee, Yongki; Liu, Hailiang
11
2015
Convergence rates for relaxation schemes approximating conservation laws. Zbl 0954.35108
Liu, Hailiang; Warnecke, Gerald
10
2000
A note on harmonic maps. Zbl 0996.58507
Liu, H.; Liao, Guojun
10
1996
Decay rate for travelling waves of a relaxation model. Zbl 0908.35074
Liu, Hailiang; Woo, Ching Wah; Yang, Tong
10
1997
On discreteness of the Hopf equation. Zbl 1149.65071
Liu, Hai-liang
10
2008
KdV dynamics in the plasma-sheath transition. Zbl 1060.76137
Liu, Hailiang; Slemrod, M.
9
2004
An entropy satisfying conservative method for the Fokker-Planck equation of the finitely extensible nonlinear elastic dumbbell model. Zbl 1422.74097
Liu, Hailiang; Yu, Hui
9
2012
Critical thresholds in hyperbolic relaxation systems. Zbl 1170.35062
Li, Tong; Liu, Hailiang
9
2009
Unconditionally energy stable DG schemes for the Swift-Hohenberg equation. Zbl 1427.65372
Liu, Hailiang; Yin, Peimeng
9
2019
An invariant preserving discontinuous Galerkin method for the Camassa-Holm equation. Zbl 1382.65321
Liu, Hailiang; Xing, Yulong
9
2016
Numerical approximation of the Euler-Poisson-Boltzmann model in the quasineutral limit. Zbl 1395.76047
Degond, P.; Liu, H.; Savelief, D.; Vignal, M.-H.
8
2012
A mixed discontinuous Galerkin method without interior penalty for time-dependent fourth order problems. Zbl 1407.65168
Liu, Hailiang; Yin, Peimeng
8
2018
The \(L^p\) stability of relaxation rarefaction profiles. Zbl 0988.35113
Liu, Hailiang
8
2001
Recovery of high frequency wave fields for the acoustic wave equation. Zbl 1213.35284
Liu, Hailiang; Ralston, James
8
2010
Global regularity of the 4D restricted Euler equations. Zbl 1193.37123
Liu, Hailiang; Tadmor, Eitan; Wei, Dongming
7
2010
Alternating evolution discontinuous Galerkin methods for Hamilton-Jacobi equations. Zbl 1349.65461
Liu, Hailiang; Pollack, Michael
7
2014
Stability of a traffic flow model with nonconvex relaxation. Zbl 1099.35156
Li, Tong; Liu, Hailiang
7
2005
A level set framework for capturing multi-valued solutions of nonlinear first-order equations. Zbl 1109.65080
Liu, Hailiang; Cheng, Li-Tien; Osher, Stanley
7
2006
Diffusion limit of a hyperbolic system with relaxation. Zbl 0922.35086
Jin, Shi; Liu, Hailiang
6
1998
Global regularity, and wave breaking phenomena in a class of nonlocal dispersive equations. Zbl 1218.35175
Liu, Hailiang; Yin, Zhaoyang
6
2010
Global well-posedness for the microscopic FENE model with a sharp boundary condition. Zbl 1233.35109
Liu, Hailiang; Shin, Jaemin
6
2012
Semiclassical limit of the nonlinear Schrödinger-Poisson equation with subcritical initial data. Zbl 1166.35374
Liu, Hailiang; Tadmor, Eitan
6
2002
Robust control of robotic manipulators based on integral sliding mode. Zbl 1154.93344
Shi, J.; Liu, H.; Bajcinca, N.
6
2008
Invariant-region-preserving DG methods for multi-dimensional hyperbolic conservation law systems, with an application to compressible Euler equations. Zbl 1416.65293
Jiang, Yi; Liu, Hailiang
6
2018
An iterative discontinuous Galerkin method for solving the nonlinear Poisson Boltzmann equation. Zbl 1388.65162
Yin, Peimeng; Huang, Yunqing; Liu, Hailiang
6
2014
Computing multi-valued velocity and electric fields for 1D Euler-Poisson equations. Zbl 1146.78012
Liu, Hailiang; Wang, Zhongming
5
2007
A field-space-based level set method for computing multi-valued solutions to 1D Euler-Poisson equations. Zbl 1140.81399
Liu, Hailiang; Wang, Zhongming
5
2007
Alternating evolution discontinuous Galerkin methods for convection-diffusion equations. Zbl 1352.65356
Liu, Hailiang; Pollack, Michael
5
2016
Alternating evolution schemes for hyperbolic conservation laws. Zbl 1248.65092
Saran, Haseena; Liu, Hailiang
5
2011
Critical thresholds in a relaxation model for traffic flows. Zbl 1152.35006
Li, Tong; Liu, Hailiang
5
2008
A nonlocal conservation law with nonlinear “radiation” inhomogeneity. Zbl 1158.35063
di Francesco, Marco; Fellner, Klemens; Liu, Hailiang
5
2008
Boundary conditions for the microscopic FENE models. Zbl 1147.76003
Liu, Chun; Liu, Hailiang
5
2008
Semi-active fuzzy sliding mode control of full vehicle and suspensions. Zbl 1182.70067
Liu, H.; Nonami, K.; Hagiwara, T.
5
2005
Tiling sets and spectral sets over finite fields. Zbl 1376.52038
Aten, C.; Ayachi, B.; Bau, E.; FitzPatrick, D.; Iosevich, A.; Liu, H.; Lott, A.; MacKinnon, I.; Maimon, S.; Nan, S.; Pakianathan, J.; Petridis, G.; Rojas Mena, C.; Sheikh, A.; Tribone, T.; Weill, J.; Yu, C.
5
2017
Superposition of multi-valued solutions in high frequency wave dynamics. Zbl 1203.65141
Liu, Hailiang; Wang, Zhongming
5
2008
On invariant-preserving finite difference schemes for the Camassa-Holm equation and the two-component Camassa-Holm system. Zbl 1388.65059
Liu, Hailiang; Pendleton, Terrance
5
2016
Critical thresholds in one-dimensional damped Euler-Poisson systems. Zbl 1453.35145
Bhatnagar, Manas; Liu, Hailiang
5
2020
Efficient, positive, and energy stable schemes for multi-d Poisson-Nernst-Planck systems. Zbl 1471.35277
Liu, Hailiang; Maimaitiyiming, Wumaier
5
2021
Nonlinear stability and existence of stationary discrete travelling waves for the relaxing schemes. Zbl 0934.65101
Liu, Hailiang; Wang, Jinghua; Yang, Tong
4
1999
Global orientation dynamics for liquid crystalline polymers. Zbl 1183.82101
Liu, Hailiang
4
2007
A conservative discontinuous Galerkin method for the Degasperis-Procesi equation. Zbl 1296.35158
Huang, Yunqing; Liu, Hailiang; Yi, Nianyu
4
2014
Gaussian beam methods for the Helmholtz equation. Zbl 1302.35135
Liu, Hailiang; Ralston, James; Runborg, Olof; Tanushev, Nicolay M.
4
2014
Long-time diffusive behavior of solutions to a hyperbolic relaxation system. Zbl 0981.35035
Liu, Hailiang; Natalini, Roberto
4
2001
Time-asymptotic stability of boundary-layers for a hyperbolic relaxation system. Zbl 0997.35007
Liu, Hailiang; Yong, Wen-An
4
2001
Critical thresholds in the semiclassical limit of 2D rotational Schrödinger equations. Zbl 1089.35052
Liu, Hailiang
4
2006
Critical thresholds in a relaxation system with resonance of characteristic speeds. Zbl 1171.35428
Li, Tong; Liu, Hailiang
4
2009
Global attractor for a nonlinear thermoviscoelastic system in shape memory alloys. Zbl 1173.35386
Qin, Yuming; Liu, Hailiang; Song, Changming
4
2008
A conservative discontinuous Galerkin method for nonlinear electromagnetic Schrödinger equations. Zbl 1435.35364
Yi, Nianyu; Huang, Yunqing; Liu, Hailiang
4
2019
Thresholds in three-dimensional restricted Euler-Poisson equations. Zbl 1434.35105
Lee, Yongki; Liu, Hailiang
4
2013
Time-asymptotic convergence rates towards the discrete evolutionary stable distribution. Zbl 1328.65268
Cai, Wenli; Jabin, Pierre-Emmanuel; Liu, Hailiang
4
2015
Threshold for shock formation in the hyperbolic Keller-Segel model. Zbl 1330.35250
Lee, Yongki; Liu, Hailiang
4
2015
Global dynamics of Bose-Einstein condensation for a model of the Kompaneets equation. Zbl 1362.37161
Levermore, C. David; Liu, Hailiang; Pego, Robert L.
4
2016
Third order maximum-principle-satisfying DG schemes for convection-diffusion problems with anisotropic diffusivity. Zbl 1452.65260
Yu, Hui; Liu, Hailiang
4
2019
On accuracy of the mass-preserving DG method to multi-dimensional Schrödinger equations. Zbl 1461.65241
Liu, Hailiang; Huang, Yunqing; Lu, Wenying; Yi, Nianyu
4
2019
Mass- and energy-conserved numerical schemes for nonlinear Schrödinger equations. Zbl 1473.65102
Feng, Xiaobing; Liu, Hailiang; Ma, Shu
4
2019
Computation of free surface waves around an arbitrary body by a Navier- Stokes solver using the pseudocompressibility technique. Zbl 0814.76066
Liu, H.; Ikehata, M.
3
1994
Pattern formation, wave propagation and stability in conservation laws with slow diffusion and fast reaction. Zbl 1065.35156
Fan, Haitao; Liu, Hailiang
3
2004
On a non-local selection-mutation model with a gradient flow structure. Zbl 1382.35313
Jabin, Pierre-Emmanuel; Liu, Hailiang
3
2017
On traveling wave solutions of the \(\theta\)-equation of dispersive type. Zbl 1304.35190
Ha, Tae Gab; Liu, Hailiang
3
2015
Efficient, positive, and energy stable schemes for multi-d Poisson-Nernst-Planck systems. Zbl 1471.35277
Liu, Hailiang; Maimaitiyiming, Wumaier
5
2021
Unconditionally energy stable discontinuous Galerkin schemes for the Cahn-Hilliard equation. Zbl 1480.65264
Liu, Hailiang; Yin, Peimeng
1
2021
Analysis of direct discontinuous Galerkin methods for multi-dimensional convection-diffusion equations. Zbl 1465.65100
Liu, Hailiang
1
2021
Critical thresholds in one-dimensional damped Euler-Poisson systems. Zbl 1453.35145
Bhatnagar, Manas; Liu, Hailiang
5
2020
Unconditional positivity-preserving and energy stable schemes for a reduced Poisson-Nernst-Planck system. Zbl 1473.65263
Liu, Hailiang; Maimaitiyiming, Wumaier
3
2020
Unconditionally energy stable DG schemes for the Swift-Hohenberg equation. Zbl 1427.65372
Liu, Hailiang; Yin, Peimeng
9
2019
A conservative discontinuous Galerkin method for nonlinear electromagnetic Schrödinger equations. Zbl 1435.35364
Yi, Nianyu; Huang, Yunqing; Liu, Hailiang
4
2019
Third order maximum-principle-satisfying DG schemes for convection-diffusion problems with anisotropic diffusivity. Zbl 1452.65260
Yu, Hui; Liu, Hailiang
4
2019
On accuracy of the mass-preserving DG method to multi-dimensional Schrödinger equations. Zbl 1461.65241
Liu, Hailiang; Huang, Yunqing; Lu, Wenying; Yi, Nianyu
4
2019
Mass- and energy-conserved numerical schemes for nonlinear Schrödinger equations. Zbl 1473.65102
Feng, Xiaobing; Liu, Hailiang; Ma, Shu
4
2019
A high order positivity preserving DG method for coagulation-fragmentation equations. Zbl 1426.65146
Liu, Hailiang; Gröpler, Robin; Warnecke, Gerald
2
2019
An invariant-region-preserving limiter for DG schemes to isentropic Euler equations. Zbl 1416.76153
Jiang, Yi; Liu, Hailiang
2
2019
Time-asymptotic convergence rates towards discrete steady states of a nonlocal selection-mutation model. Zbl 1427.35292
Cai, Wenli; Jabin, Pierre-Emmanuel; Liu, Hailiang
2
2019
A mixed discontinuous Galerkin method without interior penalty for time-dependent fourth order problems. Zbl 1407.65168
Liu, Hailiang; Yin, Peimeng
8
2018
Invariant-region-preserving DG methods for multi-dimensional hyperbolic conservation law systems, with an application to compressible Euler equations. Zbl 1416.65293
Jiang, Yi; Liu, Hailiang
6
2018
Error estimates for the AEDG method to one-dimensional linear convection-diffusion equations. Zbl 1376.65122
Liu, Hailiang; Wen, Hairui
3
2018
An invariant-region-preserving (IRP) limiter to DG methods for compressible Euler equations. Zbl 1407.65191
Jiang, Yi; Liu, Hailiang
2
2018
Error estimates of the third order Runge-Kutta alternating evolution discontinuous Galerkin method for convection-diffusion problems. Zbl 1422.65261
Liu, Hailiang; Wen, Hairui
1
2018
Error estimates for the iterative discontinuous Galerkin method to the nonlinear Poisson-Boltzmann equation. Zbl 07414376
Yin, Peimeng; Huang, Yunqing; Liu, Hailiang
1
2018
Superconvergence of the direct discontinuous Galerkin method for convection-diffusion equations. Zbl 1361.65061
Cao, Waixiang; Liu, Hailiang; Zhang, Zhimin
22
2017
A free energy satisfying discontinuous Galerkin method for one-dimensional Poisson-Nernst-Planck systems. Zbl 1406.82021
Liu, Hailiang; Wang, Zhongming
20
2017
Tiling sets and spectral sets over finite fields. Zbl 1376.52038
Aten, C.; Ayachi, B.; Bau, E.; FitzPatrick, D.; Iosevich, A.; Liu, H.; Lott, A.; MacKinnon, I.; Maimon, S.; Nan, S.; Pakianathan, J.; Petridis, G.; Rojas Mena, C.; Sheikh, A.; Tribone, T.; Weill, J.; Yu, C.
5
2017
On a non-local selection-mutation model with a gradient flow structure. Zbl 1382.35313
Jabin, Pierre-Emmanuel; Liu, Hailiang
3
2017
A finite volume method for nonlocal competition-mutation equations with a gradient flow structure. Zbl 1378.92047
Cai, Wenli; Liu, Hailiang
2
2017
On the coupling of local multilevel mesh refinement and ZZ methods for unilateral frictional contact problems in elastostatics. Zbl 1439.74219
Liu, H.; Ramière, I.; Lebon, F.
1
2017
Error estimates for Gaussian beam methods applied to symmetric strictly hyperbolic systems. Zbl 07213155
Liu, Hailiang; Pryporov, Maksym
1
2017
A Hamiltonian preserving discontinuous Galerkin method for the generalized Korteweg-de Vries equation. Zbl 1349.65462
Liu, Hailiang; Yi, Nianyu
15
2016
An entropy satisfying discontinuous Galerkin method for nonlinear Fokker-Planck equations. Zbl 1354.35158
Liu, Hailiang; Wang, Zhongming
14
2016
An invariant preserving discontinuous Galerkin method for the Camassa-Holm equation. Zbl 1382.65321
Liu, Hailiang; Xing, Yulong
9
2016
Alternating evolution discontinuous Galerkin methods for convection-diffusion equations. Zbl 1352.65356
Liu, Hailiang; Pollack, Michael
5
2016
On invariant-preserving finite difference schemes for the Camassa-Holm equation and the two-component Camassa-Holm system. Zbl 1388.65059
Liu, Hailiang; Pendleton, Terrance
5
2016
Global dynamics of Bose-Einstein condensation for a model of the Kompaneets equation. Zbl 1362.37161
Levermore, C. David; Liu, Hailiang; Pego, Robert L.
4
2016
Sobolev and max norm error estimates for Gaussian beam superpositions. Zbl 1372.35263
Liu, Hailiang; Runborg, Olof; Tanushev, Nicolay M.
2
2016
Oscillatory traveling wave solutions to an attractive chemotaxis system. Zbl 1350.35055
Li, Tong; Liu, Hailiang; Wang, Lihe
1
2016
Optimal error estimates of the direct discontinuous Galerkin method for convection-diffusion equations. Zbl 1331.65141
Liu, Hailiang
30
2015
Mass preserving discontinuous Galerkin methods for Schrödinger equations. Zbl 1352.65358
Lu, Wenying; Huang, Yunqing; Liu, Hailiang
20
2015
A local discontinuous Galerkin method for the Burgers-Poisson equation. Zbl 1339.65177
Liu, Hailiang; Ploymaklam, Nattapol
18
2015
The entropy satisfying discontinuous Galerkin method for Fokker-Planck equations. Zbl 1320.65143
Liu, Hailiang; Yu, Hui
17
2015
Thresholds for shock formation in traffic flow models with Arrhenius look-ahead dynamics. Zbl 1304.35420
Lee, Yongki; Liu, Hailiang
11
2015
Time-asymptotic convergence rates towards the discrete evolutionary stable distribution. Zbl 1328.65268
Cai, Wenli; Jabin, Pierre-Emmanuel; Liu, Hailiang
4
2015
Threshold for shock formation in the hyperbolic Keller-Segel model. Zbl 1330.35250
Lee, Yongki; Liu, Hailiang
4
2015
On traveling wave solutions of the \(\theta\)-equation of dispersive type. Zbl 1304.35190
Ha, Tae Gab; Liu, Hailiang
3
2015
Entropy satisfying schemes for computing selection dynamics in competitive interactions. Zbl 1318.65085
Liu, Hailiang; Cai, Wenli; Su, Ning
3
2015
Error estimates of the Bloch band-based Gaussian beam superposition for the Schrödinger equation. Zbl 1348.35213
Liu, Hailiang; Pryporov, Maksym
2
2015
A free energy satisfying finite difference method for Poisson-Nernst-Planck equations. Zbl 1349.65317
Liu, Hailiang; Wang, Zhongming
33
2014
Maximum-principle-satisfying third order discontinuous Galerkin schemes for Fokker-Planck equations. Zbl 1341.65038
Liu, Hailiang; Yu, Hui
18
2014
Alternating evolution discontinuous Galerkin methods for Hamilton-Jacobi equations. Zbl 1349.65461
Liu, Hailiang; Pollack, Michael
7
2014
An iterative discontinuous Galerkin method for solving the nonlinear Poisson Boltzmann equation. Zbl 1388.65162
Yin, Peimeng; Huang, Yunqing; Liu, Hailiang
6
2014
A conservative discontinuous Galerkin method for the Degasperis-Procesi equation. Zbl 1296.35158
Huang, Yunqing; Liu, Hailiang; Yi, Nianyu
4
2014
Gaussian beam methods for the Helmholtz equation. Zbl 1302.35135
Liu, Hailiang; Ralston, James; Runborg, Olof; Tanushev, Nicolay M.
4
2014
Entropy/energy stable schemes for evolutionary dispersal models. Zbl 1349.65318
Liu, Hailiang; Yu, Hui
1
2014
Numerical simulations of traveling wave solutions in a drift paradox inspired diffusive delay population model. Zbl 07312544
Jackiewicz, Z.; Liu, H.; Li, B.; Kuang, Y.
1
2014
A direct discontinuous Galerkin method for the generalized Korteweg-de Vries equation: energy conservation and boundary effect. Zbl 1297.65122
Yi, Nianyu; Huang, Yunqing; Liu, Hailiang
25
2013
Error estimates for Gaussian beam superpositions. Zbl 1277.35236
Liu, Hailiang; Runborg, Olof; Tanushev, Nicolay M.
21
2013
Thresholds in three-dimensional restricted Euler-Poisson equations. Zbl 1434.35105
Lee, Yongki; Liu, Hailiang
4
2013
A uniform multiscale method for 2D static and dynamic analyses of heterogeneous materials. Zbl 1352.74459
Zhang, H. W.; Liu, H.; Wu, J. K.
3
2013
Alternating evolution schemes for Hamilton-Jacobi equations. Zbl 1270.65049
Liu, Hailiang; Pollack, Michael; Saran, Haseena
2
2013
Recovery of normal derivatives from the piecewise \(L^2\) projection. Zbl 1408.65009
Huang, Yunqing; Liu, Hailiang; Yi, Nianyu
12
2012
An entropy satisfying conservative method for the Fokker-Planck equation of the finitely extensible nonlinear elastic dumbbell model. Zbl 1422.74097
Liu, Hailiang; Yu, Hui
9
2012
Numerical approximation of the Euler-Poisson-Boltzmann model in the quasineutral limit. Zbl 1395.76047
Degond, P.; Liu, H.; Savelief, D.; Vignal, M.-H.
8
2012
Global well-posedness for the microscopic FENE model with a sharp boundary condition. Zbl 1233.35109
Liu, Hailiang; Shin, Jaemin
6
2012
The Cauchy-Dirichlet problem for the finitely extensible nonlinear elastic dumbbell model of polymeric fluids. Zbl 1257.35144
Liu, Hailiang; Shin, Jaemin
2
2012
Alternating evolution schemes for hyperbolic conservation laws. Zbl 1248.65092
Saran, Haseena; Liu, Hailiang
5
2011
A level set approach for dilute non-collisional fluid-particle flows. Zbl 1391.76348
Liu, Hailiang; Wang, Zhongming; Fox, Rodney O.
1
2011
The direct discontinuous Galerkin (DDG) method for diffusion with interface corrections. Zbl 1364.65200
Liu, Hailiang; Yan, Jue
68
2010
Recovery of high frequency wave fields from phase space-based measurements. Zbl 1221.35031
Liu, Hailiang; Ralston, James
12
2010
Recovery of high frequency wave fields for the acoustic wave equation. Zbl 1213.35284
Liu, Hailiang; Ralston, James
8
2010
Global regularity of the 4D restricted Euler equations. Zbl 1193.37123
Liu, Hailiang; Tadmor, Eitan; Wei, Dongming
7
2010
Global regularity, and wave breaking phenomena in a class of nonlocal dispersive equations. Zbl 1218.35175
Liu, Hailiang; Yin, Zhaoyang
6
2010
The direct discontinuous Galerkin (DDG) methods for diffusion problems. Zbl 1189.65227
Liu, Hailiang; Yan, Jue
85
2009
Kinetic models for polymers with inertial effects. Zbl 1183.76614
Degond, Pierre; Liu, Hailiang
12
2009
Critical thresholds in hyperbolic relaxation systems. Zbl 1170.35062
Li, Tong; Liu, Hailiang
9
2009
Critical thresholds in a relaxation system with resonance of characteristic speeds. Zbl 1171.35428
Li, Tong; Liu, Hailiang
4
2009
Development of an analytical \(\beta\)-function PDF integration algorithm for simulation of non-premixed turbulent combustion. Zbl 1405.80011
Lien, F. S.; Liu, H.; Chui, E.; McCartney, C. J.
1
2009
Computational aerodynamics of low Reynolds number plunging, pitching and flexible wings for MAV applications. Zbl 1271.76285
Shyy, W.; Lian, Y.; Tang, J.; Liu, H.; Trizila, P.; Stanford, B.; Bernal, L.; Cesnik, C.; Friedmann, P.; Ifju, P.
15
2008
On discreteness of the Hopf equation. Zbl 1149.65071
Liu, Hai-liang
10
2008
Robust control of robotic manipulators based on integral sliding mode. Zbl 1154.93344
Shi, J.; Liu, H.; Bajcinca, N.
6
2008
Critical thresholds in a relaxation model for traffic flows. Zbl 1152.35006
Li, Tong; Liu, Hailiang
5
2008
A nonlocal conservation law with nonlinear “radiation” inhomogeneity. Zbl 1158.35063
di Francesco, Marco; Fellner, Klemens; Liu, Hailiang
5
2008
Boundary conditions for the microscopic FENE models. Zbl 1147.76003
Liu, Chun; Liu, Hailiang
5
2008
Superposition of multi-valued solutions in high frequency wave dynamics. Zbl 1203.65141
Liu, Hailiang; Wang, Zhongming
5
2008
Global attractor for a nonlinear thermoviscoelastic system in shape memory alloys. Zbl 1173.35386
Qin, Yuming; Liu, Hailiang; Song, Changming
4
2008
An alternating evolution approximation to systems of hyperbolic conservation laws. Zbl 1162.35049
Liu, Hailiang
3
2008
Rigorous derivation of the hydrodynamical equations for rotating superfluids. Zbl 1144.81462
Liu, Hailiang; Sparber, Christof
2
2008
A Bloch band based level set method for computing the semiclassical limit of Schrödinger equations. Zbl 1168.65056
Liu, Hailiang; Wang, Zhongming
1
2008
Computing multi-valued velocity and electric fields for 1D Euler-Poisson equations. Zbl 1146.78012
Liu, Hailiang; Wang, Zhongming
5
2007
A field-space-based level set method for computing multi-valued solutions to 1D Euler-Poisson equations. Zbl 1140.81399
Liu, Hailiang; Wang, Zhongming
5
2007
Global orientation dynamics for liquid crystalline polymers. Zbl 1183.82101
Liu, Hailiang
4
2007
The modular multisensory DLR-HIT-Hand. Zbl 1183.70026
Liu, H.; Meusel, P.; Seitz, N.; Willberg, B.; Hirzinger, G.; Jin, M. H.; Liu, Y. W.; Wei, R.; Xie, Z. W.
1
2007
A local discontinuous Galerkin method for the Korteweg-de Vries equation with boundary effect. Zbl 1092.65083
Liu, Hailiang; Yan, Jue
26
2006
Wave breaking in a class of nonlocal dispersive wave equations. Zbl 1110.35069
Liu, Hailiang
23
2006
Multi-valued solution and level set methods in computational high frequency wave propagation. Zbl 1120.65110
Liu, H.; Osher, S.; Tsai, R.
13
2006
A level set framework for capturing multi-valued solutions of nonlinear first-order equations. Zbl 1109.65080
Liu, Hailiang; Cheng, Li-Tien; Osher, Stanley
7
2006
Critical thresholds in the semiclassical limit of 2D rotational Schrödinger equations. Zbl 1089.35052
Liu, Hailiang
4
2006
Sharp interface Cartesian grid method. I: An easily implemented technique for 3D moving boundary computations. Zbl 1154.76359
Marella, S.; Krishnan, S.; Liu, H.; Udaykumar, H. S.
72
2005
Sharp interface Cartesian grid method. II: A technique for simulating droplet interactions with surfaces of arbitrary shape. Zbl 1154.76358
Liu, H.; Krishnan, S.; Marella, S.; Udaykumar, H. S.
35
2005
Computing multivalued physical observables for the semiclassical limit of the Schrödinger equation. Zbl 1072.65132
Jin, Shi; Liu, Hailiang; Osher, Stanley; Tsai, Yen-Hsi Richard
35
2005
Axial symmetry and classification of stationary solutions of Doi-Onsager equation on the sphere with Maier-Saupe potential. Zbl 1092.76007
Liu, Hailiang; Zhang, Hui; Zhang, Pingwen
26
2005
Computing multi-valued physical observables for the high frequency limit of symmetric hyperbolic systems. Zbl 1098.65094
Jin, Shi; Liu, Hailiang; Osher, Stanley; Tsai, Richard
20
2005
Stability of a traffic flow model with nonconvex relaxation. Zbl 1099.35156
Li, Tong; Liu, Hailiang
7
2005
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Cited by 990 Authors

76 Liu, Hailiang
21 Shen, Chun
20 Yang, Hanchun
18 Sun, Meina
17 Shu, Chi-Wang
16 Zhang, Yu
15 Huang, Yunqing
14 Yi, Nianyu
12 Cheng, Hongjun
12 Jin, Shi
12 Yin, Gan
11 Liu, Tiegang
11 Wang, Jinhuan
11 Wang, Zhongming
11 Yan, Jue
10 Zhang, Yanyan
9 Cheng, Jian
9 Guo, Lihui
9 Shao, Zhiqiang
9 Yu, Xijun
9 Zhang, Pingwen
8 Huang, Chaobao
8 Li, Tong
8 Pang, Yicheng
8 Tadmor, Eitan
8 Xu, Yan
7 An, Na
7 Cheng, Yingda
7 Choi, Young-Pil
7 Lee, Yongki
7 Meng, Xiong
7 Nedeljkov, Marko
7 Runborg, Olof
7 Yin, Peimeng
6 Carrillo de la Plata, José Antonio
6 Degond, Pierre
6 Fox, Rodney O.
6 Osher, Stanley Joel
6 Sarrico, Carlos Orlando R.
6 Sheng, Wancheng
6 Tan, Changhui
6 Wang, Wei
6 Wu, Boying
6 Yang, Xu
5 Cheng, Yao
5 Liu, Jinjing
5 Luo, Hong
5 Mitrovic, Darko
5 Qian, Jianliang
5 Rozanova, Olga S.
5 Süli, Endre E.
5 Titi, Edriss Saleh
5 Wen, Xin
5 Xia, Yinhua
5 Xing, Yulong
5 Zhang, Mengping
5 Zhang, Qian
5 Zhang, Rongpei
5 Zhang, Zhiyue
5 Zhou, Shenggao
5 Zhou, Zhennan
5 Zhu, Changjiang
4 Baccouch, Mahboub
4 Barrett, John W.
4 Bhatnagar, Manas
4 Dai, Limei
4 Du, Qiang
4 Gosse, Laurent
4 He, Dongdong
4 Kim, Junseok
4 Kwon, Bongsuk
4 Motamed, Mohammad
4 Nishikawa, Hiroaki
4 Pan, Kejia
4 Pu, Xueke
4 Ruan, Lizhi
4 Shu, Shi
4 Tao, Qi
4 Tsai, Yen-Hsi Richard
4 Xu, Jie
4 Yan, Jinliang
4 Yang, Ying
4 Yong, Wen-An
4 Yu, Hui
4 Yue, Huiqiang
4 Yuen, Manwai
4 Zhang, Dazhi
4 Zhang, Fan
4 Zhang, Qiang
4 Zhang, Zhifei
4 Zhou, Hong
4 Zhu, Jiang
3 Barbieri, Luca
3 Cao, Waixiang
3 Chen, Zheng
3 Cheng, Bin
3 Cockburn, Bernardo
3 Dehghan Takht Fooladi, Mehdi
3 Feng, Xiaobing
3 Gottlieb, Sigal
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52 Journal of Scientific Computing
50 Journal of Differential Equations
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20 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods
20 Communications in Computational Physics
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10 SIAM Journal on Numerical Analysis
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6 Chinese Annals of Mathematics. Series B
6 Computational and Applied Mathematics
6 Bulletin of the Malaysian Mathematical Sciences Society. Second Series
5 Communications in Mathematical Physics
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5 Communications on Pure and Applied Mathematics
5 SIAM Journal on Applied Mathematics
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3 Multiscale Modeling & Simulation
3 Kinetic and Related Models
3 Open Mathematics
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2 ZAMM. Zeitschrift für Angewandte Mathematik und Mechanik
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2 Discrete and Continuous Dynamical Systems. Series B
2 Comptes Rendus. Mathématique. Académie des Sciences, Paris
2 Thai Journal of Mathematics
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