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Liu, Hailiang

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Author ID: liu.hailiang Recent zbMATH articles by "Liu, Hailiang"
Published as: Liu, Hailiang; Liu, H.; Liu, Hai-liang; Liu, H. L.
Documents Indexed: 185 Publications since 1976
all top 5

Co-Authors

24 single-authored
9 Wang, Jinghua
8 Tadmor, Eitan
8 Wang, Zhongming
7 Huang, Yunqing
6 Warnecke, Gerald G.
6 Yi, Nianyu
5 Li, Tong
5 Osher, Stanley Joel
5 Yin, Peimeng
5 Yu, Hui
4 Cai, Wenli
4 Jin, Shi
4 Ralston, James V.
4 Yang, Tong
3 Jabin, Pierre-Emmanuel
3 Jiang, Yi
3 Lee, Yongki
3 Pollack, Michael
3 Runborg, Olof
3 Tanushev, Nicolay M.
3 Tsai, Yen-Hsi Richard
3 Yan, Jue
2 Bernussou, Jacques
2 Bhatnagar, Manas
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 Shin, Jaemin
2 Udaykumar, Holavanahalli S.
2 Wen, Hairui
2 Yamaguchi, Takami
1 Akulichev, Victor A.
1 Aten, Charlotte
1 Ates, Muzaffer
1 Ayachi, B.
1 Bajcinca, Naim
1 Bau, E.
1 Bazargan-Sabet, B.
1 Butterfaß, J.
1 Cao, Waixiang
1 Cesnik, Carlos E. S.
1 Chanchole, S.
1 Chui, E.
1 Davulcu, Hasan
1 Di Francesco, Marco
1 Dirr, Bodo
1 Engelberg, Shlomo
1 Fan, Haitao
1 Fellner, Klemens
1 Fox, Rodney O.
1 Garg, Hari Krishna
1 Gröpler, Robin
1 Ha, Tae Gab
1 Ifju, Peter G.
1 Ikehata, Masaru
1 Iosevich, Alex
1 Jackiewicz, Zdzislaw
1 Knoch, S.
1 Kolippakkam, D.
1 Kuang, Yang
1 Lebon, Frédéric
1 Levermore, C. David
1 Li, Bingtuan
1 Lian, Yongsheng
1 Liao, Guojun
1 Lien, Fue-Sang
1 Liu, Chun
1 Lott, Adam
1 MacKinnon, I.
1 Maimaitiyiming, Wumaier
1 Maimon, Shir
1 Markowich, Peter Alexander
1 McCartney, C. J.
1 Mehl, Michael J.
1 Meusel, P.
1 Mira, Christian
1 Mu, S. Y.
1 Natalini, Roberto
1 Nguyen, Hung V.
1 Nonami, Kenzo
1 Papaconstantopoulos, D. A.
1 Pego, Robert L.
1 Pendleton, Terrance
1 Petridis, Giorgis
1 Ploymaklam, Nattapol
1 Popp, Karl Karl
1 Qian, Linrui
1 Qin, Yuming
1 Ramière, Isabelle
1 Rojas Mena, C.
1 Savelief, D.
...and 23 more Co-Authors
all top 5

Serials

21 Journal of Computational Physics
8 Mathematics of Computation
8 Journal of Differential Equations
8 Journal of Scientific Computing
6 SIAM Journal on Scientific Computing
5 SIAM Journal on Numerical Analysis
5 Physica D
5 Applied Mathematics Letters
5 SIAM Journal on Mathematical Analysis
4 M\(^3\)AS. Mathematical Models & Methods in Applied Sciences
4 Communications in Mathematical Sciences
4 Communications in Computational Physics
3 International Journal for Numerical Methods in Fluids
3 International Journal of Solids and Structures
3 Journal of Computational and Applied Mathematics
3 Numerische Mathematik
3 Numerical Methods for Partial Differential Equations
3 SIAM Journal on Applied Mathematics
3 Methods and Applications of Analysis
3 Discrete and Continuous Dynamical Systems
3 Journal of Hyperbolic Differential Equations
2 Journal of Mathematical Analysis and Applications
2 Molecular Simulation
2 Indiana University Mathematics Journal
2 Acta Mathematica Hungarica
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 Computers and Structures
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 Sound and Vibration
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 Acta Mathematicae Applicatae Sinica
1 Circuits, Systems, and Signal Processing
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 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 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 Iranian Journal of Fuzzy Systems
1 Acta Mechanica Sinica
1 Networks and Heterogeneous Media
1 Journal of Nonlinear Science and Applications
1 Quantum Studies: Mathematics and Foundations

Publications by Year

Citations contained in zbMATH Open

136 Publications have been cited 1,510 times in 686 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
157
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
77
2004
The direct discontinuous Galerkin (DDG) methods for diffusion problems. Zbl 1189.65227
Liu, Hailiang; Yan, Jue
69
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.
67
2005
The direct discontinuous Galerkin (DDG) method for diffusion with interface corrections. Zbl 1364.65200
Liu, Hailiang; Yan, Jue
51
2010
Critical thresholds in Euler-Poisson equations. Zbl 0989.35110
Engelberg, Shlomo; Liu, Hailiang; Tadmor, Eitan
48
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
Critical thresholds in a convolution model for nonlinear conservation laws. Zbl 1002.35085
Liu, Hailiang; Tadmor, Eitan
36
2001
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
Spectral dynamics of the velocity gradient field in restricted flows. Zbl 1031.76006
Liu, Hailiang; Tadmor, Eitan
33
2002
A numerical study of insect flight. Zbl 0929.76092
Liu, H.; Kawachi, K.
33
1998
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.
33
2005
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.
30
2001
A numerical study of undulatory swimming. Zbl 0958.76099
Liu, H.; Kawachi, K.
28
1999
Critical thresholds in 2D restricted Euler-Poisson equations. Zbl 1073.35187
Liu, Hailiang; Tadmor, Eitan
27
2003
A local discontinuous Galerkin method for the Korteweg-de Vries equation with boundary effect. Zbl 1092.65083
Liu, Hailiang; Yan, Jue
24
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
24
2005
Wave breaking in a class of nonlocal dispersive wave equations. Zbl 1110.35069
Liu, Hailiang
22
2006
A free energy satisfying finite difference method for Poisson-Nernst-Planck equations. Zbl 1349.65317
Liu, Hailiang; Wang, Zhongming
22
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
21
2013
Optimal error estimates of the direct discontinuous Galerkin method for convection-diffusion equations. Zbl 1331.65141
Liu, Hailiang
21
2015
Rotation prevents finite-time breakdown. Zbl 1098.76643
Liu, Hailiang; Tadmor, Eitan
21
2004
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
Error estimates for Gaussian beam superpositions. Zbl 1277.35236
Liu, Hailiang; Runborg, Olof; Tanushev, Nicolay M.
18
2013
The entropy satisfying discontinuous Galerkin method for Fokker-Planck equations. Zbl 1320.65143
Liu, Hailiang; Yu, Hui
15
2015
Superconvergence of the direct discontinuous Galerkin method for convection-diffusion equations. Zbl 1361.65061
Cao, Waixiang; Liu, Hailiang; Zhang, Zhimin
14
2017
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.
14
2008
A local discontinuous Galerkin method for the Burgers-Poisson equation. Zbl 1339.65177
Liu, Hailiang; Ploymaklam, Nattapol
13
2015
Mass preserving discontinuous Galerkin methods for Schrödinger equations. Zbl 1352.65358
Lu, Wenying; Huang, Yunqing; Liu, Hailiang
13
2015
Multi-valued solution and level set methods in computational high frequency wave propagation. Zbl 1120.65110
Liu, H.; Osher, S.; Tsai, R.
13
2006
Entropy-based fuzzy clustering and fuzzy modeling. Zbl 1147.62348
Yao, J.; Dash, M.; Tan, S. T.; Liu, H.
12
2000
Asymptotic stability of relaxation shock profiles for hyperbolic conservation laws. Zbl 1039.35063
Liu, Hailiang
12
2003
Recovery of high frequency wave fields from phase space-based measurements. Zbl 1221.35031
Liu, Hailiang; Ralston, James
12
2010
Maximum-principle-satisfying third order discontinuous Galerkin schemes for Fokker-Planck equations. Zbl 1341.65038
Liu, Hailiang; Yu, Hui
12
2014
Stability of a relaxation model with a nonconvex flux. Zbl 0961.35017
Liu, Hailiang; Wang, Jinghua; Yang, Tong
12
1998
Kinetic models for polymers with inertial effects. Zbl 1183.76614
Degond, Pierre; Liu, Hailiang
12
2009
A free energy satisfying discontinuous Galerkin method for one-dimensional Poisson-Nernst-Planck systems. Zbl 1406.82021
Liu, Hailiang; Wang, Zhongming
12
2017
An entropy satisfying discontinuous Galerkin method for nonlinear Fokker-Planck equations. Zbl 1354.35158
Liu, Hailiang; Wang, Zhongming
12
2016
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
Convergence rates for relaxation schemes approximating conservation laws. Zbl 0954.35108
Liu, Hailiang; Warnecke, Gerald
10
2000
Surfaces in the lightlike cone. Zbl 1108.53011
Liu, H. L.
10
2007
Recovery of normal derivatives from the piecewise \(L^2\) projection. Zbl 1408.65009
Huang, Yunqing; Liu, Hailiang; Yi, Nianyu
10
2012
On discreteness of the Hopf equation. Zbl 1149.65071
Liu, Hai-liang
9
2008
A Hamiltonian preserving discontinuous Galerkin method for the generalized Korteweg-de Vries equation. Zbl 1349.65462
Liu, Hailiang; Yi, Nianyu
9
2016
KdV dynamics in the plasma-sheath transition. Zbl 1060.76137
Liu, Hailiang; Slemrod, M.
9
2004
Recovery of high frequency wave fields for the acoustic wave equation. Zbl 1213.35284
Liu, Hailiang; Ralston, James
8
2010
Thresholds for shock formation in traffic flow models with Arrhenius look-ahead dynamics. Zbl 1304.35420
Lee, Yongki; Liu, Hailiang
8
2015
An invariant preserving discontinuous Galerkin method for the Camassa-Holm equation. Zbl 1382.65321
Liu, Hailiang; Xing, Yulong
8
2016
The \(L^p\) stability of relaxation rarefaction profiles. Zbl 0988.35113
Liu, Hailiang
8
2001
Critical thresholds in hyperbolic relaxation systems. Zbl 1170.35062
Li, Tong; Liu, Hailiang
8
2009
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
8
2012
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
Stability of a traffic flow model with nonconvex relaxation. Zbl 1099.35156
Li, Tong; Liu, Hailiang
6
2005
Semiclassical limit of the nonlinear Schrödinger-Poisson equation with subcritical initial data. Zbl 1166.35374
Liu, Hailiang; Tadmor, Eitan
6
2002
Alternating evolution discontinuous Galerkin methods for Hamilton-Jacobi equations. Zbl 1349.65461
Liu, Hailiang; Pollack, Michael
6
2014
Global regularity, and wave breaking phenomena in a class of nonlocal dispersive equations. Zbl 1218.35175
Liu, Hailiang; Yin, Zhaoyang
6
2010
Global regularity of the 4D restricted Euler equations. Zbl 1193.37123
Liu, Hailiang; Tadmor, Eitan; Wei, Dongming
6
2010
Robust control of robotic manipulators based on integral sliding mode. Zbl 1154.93344
Shi, J.; Liu, H.; Bajcinca, N.
6
2008
Numerical approximation of the Euler-Poisson-Boltzmann model in the quasineutral limit. Zbl 1395.76047
Degond, P.; Liu, H.; Savelief, D.; Vignal, M.-H.
6
2012
Global well-posedness for the microscopic FENE model with a sharp boundary condition. Zbl 1233.35109
Liu, Hailiang; Shin, Jaemin
6
2012
Boundary conditions for the microscopic FENE models. Zbl 1147.76003
Liu, Chun; Liu, Hailiang
5
2008
Diffusion limit of a hyperbolic system with relaxation. Zbl 0922.35086
Jin, Shi; Liu, Hailiang
5
1998
Computing multi-valued velocity and electric fields for 1D Euler-Poisson equations. Zbl 1146.78012
Liu, Hailiang; Wang, Zhongming
5
2007
Superposition of multi-valued solutions in high frequency wave dynamics. Zbl 1203.65141
Liu, Hailiang; Wang, Zhongming
5
2008
Alternating evolution discontinuous Galerkin methods for convection-diffusion equations. Zbl 1352.65356
Liu, Hailiang; Pollack, Michael
5
2016
Semi-active fuzzy sliding mode control of full vehicle and suspensions. Zbl 1182.70067
Liu, H.; Nonami, K.; Hagiwara, T.
5
2005
A mixed discontinuous Galerkin method without interior penalty for time-dependent fourth order problems. Zbl 1407.65168
Liu, Hailiang; Yin, Peimeng
5
2018
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 schemes for hyperbolic conservation laws. Zbl 1248.65092
Saran, Haseena; Liu, Hailiang
5
2011
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
A nonlocal conservation law with nonlinear “radiation” inhomogeneity. Zbl 1158.35063
di Francesco, Marco; Fellner, Klemens; Liu, Hailiang
5
2008
Global orientation dynamics for liquid crystalline polymers. Zbl 1183.82101
Liu, Hailiang
4
2007
Critical thresholds in the semiclassical limit of 2D rotational Schrödinger equations. Zbl 1089.35052
Liu, Hailiang
4
2006
An iterative discontinuous Galerkin method for solving the nonlinear Poisson Boltzmann equation. Zbl 1388.65162
Yin, Peimeng; Huang, Yunqing; Liu, Hailiang
4
2014
Gaussian beam methods for the Helmholtz equation. Zbl 1302.35135
Liu, Hailiang; Ralston, James; Runborg, Olof; Tanushev, Nicolay M.
4
2014
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
Time-asymptotic stability of boundary-layers for a hyperbolic relaxation system. Zbl 0997.35007
Liu, Hailiang; Yong, Wen-An
4
2001
Nonlinear stability and existence of stationary discrete travelling waves for the relaxing schemes. Zbl 0934.65101
Liu, Hailiang; Wang, Jinghua; Yang, Tong
4
1999
Long-time diffusive behavior of solutions to a hyperbolic relaxation system. Zbl 0981.35035
Liu, Hailiang; Natalini, Roberto
4
2001
Global attractor for a nonlinear thermoviscoelastic system in shape memory alloys. Zbl 1173.35386
Qin, Yuming; Liu, Hailiang; Song, Changming
4
2008
Critical thresholds in a relaxation model for traffic flows. Zbl 1152.35006
Li, Tong; Liu, Hailiang
4
2008
Error estimates for the AEDG method to one-dimensional linear convection-diffusion equations. Zbl 1376.65122
Liu, Hailiang; Wen, Hairui
3
2018
A conservative discontinuous Galerkin method for the Degasperis-Procesi equation. Zbl 1296.35158
Huang, Yunqing; Liu, Hailiang; Yi, Nianyu
3
2014
On traveling wave solutions of the \(\theta\)-equation of dispersive type. Zbl 1304.35190
Ha, Tae Gab; Liu, Hailiang
3
2015
Time-asymptotic convergence rates towards the discrete evolutionary stable distribution. Zbl 1328.65268
Cai, Wenli; Jabin, Pierre-Emmanuel; Liu, Hailiang
3
2015
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
Asymptotic stability of shock profiles for nonconvex convection-diffusion equation. Zbl 0888.35052
Liu, Hailiang
3
1997
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
Critical thresholds in one-dimensional damped Euler-Poisson systems. Zbl 1453.35145
Bhatnagar, Manas; Liu, Hailiang
3
2020
Critical thresholds in a relaxation system with resonance of characteristic speeds. Zbl 1171.35428
Li, Tong; Liu, Hailiang
3
2009
Threshold for shock formation in the hyperbolic Keller-Segel model. Zbl 1330.35250
Lee, Yongki; Liu, Hailiang
3
2015
An alternating evolution approximation to systems of hyperbolic conservation laws. Zbl 1162.35049
Liu, Hailiang
3
2008
Unconditionally energy stable DG schemes for the Swift-Hohenberg equation. Zbl 1427.65372
Liu, Hailiang; Yin, Peimeng
3
2019
Effect of a biasing electric field on the propagation of antisymmetric Lamb waves in piezoelectric plates. Zbl 1036.74027
Liu, H.; Wang, T. J.; Wang, Z. K.; Kuang, Z. B.
2
2002
Convergence rates to traveling waves for viscous conservation laws with dispersion. Zbl 1019.35018
Pan, Jun; Liu, Hailiang
2
2003
Relaxation dynamics, scaling limits and convergence of relaxation schemes. Zbl 1094.35078
Liu, Hailiang
2
2005
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
2
2016
On a non-local selection-mutation model with a gradient flow structure. Zbl 1382.35313
Jabin, Pierre-Emmanuel; Liu, Hailiang
2
2017
Efficient, positive, and energy stable schemes for multi-d Poisson-Nernst-Planck systems. Zbl 07358941
Liu, Hailiang; Maimaitiyiming, Wumaier
2
2021
Critical thresholds in one-dimensional damped Euler-Poisson systems. Zbl 1453.35145
Bhatnagar, Manas; Liu, Hailiang
3
2020
Unconditionally energy stable DG schemes for the Swift-Hohenberg equation. Zbl 1427.65372
Liu, Hailiang; Yin, Peimeng
3
2019
Third order maximum-principle-satisfying DG schemes for convection-diffusion problems with anisotropic diffusivity. Zbl 1452.65260
Yu, Hui; Liu, Hailiang
2
2019
A conservative discontinuous Galerkin method for nonlinear electromagnetic Schrödinger equations. Zbl 1435.35364
Yi, Nianyu; Huang, Yunqing; Liu, Hailiang
1
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
1
2019
A mixed discontinuous Galerkin method without interior penalty for time-dependent fourth order problems. Zbl 1407.65168
Liu, Hailiang; Yin, Peimeng
5
2018
Error estimates for the AEDG method to one-dimensional linear convection-diffusion equations. Zbl 1376.65122
Liu, Hailiang; Wen, Hairui
3
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
2
2018
An invariant-region-preserving (IRP) limiter to DG methods for compressible Euler equations. Zbl 1407.65191
Jiang, Yi; Liu, Hailiang
1
2018
Superconvergence of the direct discontinuous Galerkin method for convection-diffusion equations. Zbl 1361.65061
Cao, Waixiang; Liu, Hailiang; Zhang, Zhimin
14
2017
A free energy satisfying discontinuous Galerkin method for one-dimensional Poisson-Nernst-Planck systems. Zbl 1406.82021
Liu, Hailiang; Wang, Zhongming
12
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
2
2017
A finite volume method for nonlocal competition-mutation equations with a gradient flow structure. Zbl 1378.92047
Cai, Wenli; Liu, Hailiang
1
2017
Error estimates for Gaussian beam methods applied to symmetric strictly hyperbolic systems. Zbl 07213155
Liu, Hailiang; Pryporov, Maksym
1
2017
An entropy satisfying discontinuous Galerkin method for nonlinear Fokker-Planck equations. Zbl 1354.35158
Liu, Hailiang; Wang, Zhongming
12
2016
A Hamiltonian preserving discontinuous Galerkin method for the generalized Korteweg-de Vries equation. Zbl 1349.65462
Liu, Hailiang; Yi, Nianyu
9
2016
An invariant preserving discontinuous Galerkin method for the Camassa-Holm equation. Zbl 1382.65321
Liu, Hailiang; Xing, Yulong
8
2016
Alternating evolution discontinuous Galerkin methods for convection-diffusion equations. Zbl 1352.65356
Liu, Hailiang; Pollack, Michael
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
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
2
2016
Sobolev and max norm error estimates for Gaussian beam superpositions. Zbl 1372.35263
Liu, Hailiang; Runborg, Olof; Tanushev, Nicolay M.
2
2016
Lightcone dual surfaces and hyperbolic dual surfaces of spacelike curves in de Sitter 3-space. Zbl 1346.53022
Liu, H.; Pei, D.
1
2016
Optimal error estimates of the direct discontinuous Galerkin method for convection-diffusion equations. Zbl 1331.65141
Liu, Hailiang
21
2015
The entropy satisfying discontinuous Galerkin method for Fokker-Planck equations. Zbl 1320.65143
Liu, Hailiang; Yu, Hui
15
2015
A local discontinuous Galerkin method for the Burgers-Poisson equation. Zbl 1339.65177
Liu, Hailiang; Ploymaklam, Nattapol
13
2015
Mass preserving discontinuous Galerkin methods for Schrödinger equations. Zbl 1352.65358
Lu, Wenying; Huang, Yunqing; Liu, Hailiang
13
2015
Thresholds for shock formation in traffic flow models with Arrhenius look-ahead dynamics. Zbl 1304.35420
Lee, Yongki; Liu, Hailiang
8
2015
On traveling wave solutions of the \(\theta\)-equation of dispersive type. Zbl 1304.35190
Ha, Tae Gab; Liu, Hailiang
3
2015
Time-asymptotic convergence rates towards the discrete evolutionary stable distribution. Zbl 1328.65268
Cai, Wenli; Jabin, Pierre-Emmanuel; Liu, Hailiang
3
2015
Threshold for shock formation in the hyperbolic Keller-Segel model. Zbl 1330.35250
Lee, Yongki; Liu, Hailiang
3
2015
Entropy satisfying schemes for computing selection dynamics in competitive interactions. Zbl 1318.65085
Liu, Hailiang; Cai, Wenli; Su, Ning
2
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
22
2014
Maximum-principle-satisfying third order discontinuous Galerkin schemes for Fokker-Planck equations. Zbl 1341.65038
Liu, Hailiang; Yu, Hui
12
2014
Alternating evolution discontinuous Galerkin methods for Hamilton-Jacobi equations. Zbl 1349.65461
Liu, Hailiang; Pollack, Michael
6
2014
An iterative discontinuous Galerkin method for solving the nonlinear Poisson Boltzmann equation. Zbl 1388.65162
Yin, Peimeng; Huang, Yunqing; Liu, Hailiang
4
2014
Gaussian beam methods for the Helmholtz equation. Zbl 1302.35135
Liu, Hailiang; Ralston, James; Runborg, Olof; Tanushev, Nicolay M.
4
2014
A conservative discontinuous Galerkin method for the Degasperis-Procesi equation. Zbl 1296.35158
Huang, Yunqing; Liu, Hailiang; Yi, Nianyu
3
2014
Entropy/energy stable schemes for evolutionary dispersal models. Zbl 1349.65318
Liu, Hailiang; Yu, Hui
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
21
2013
Error estimates for Gaussian beam superpositions. Zbl 1277.35236
Liu, Hailiang; Runborg, Olof; Tanushev, Nicolay M.
18
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
Thresholds in three-dimensional restricted Euler-Poisson equations. Zbl 1434.35105
Lee, Yongki; Liu, Hailiang
2
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
10
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
8
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.
6
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
51
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, and wave breaking phenomena in a class of nonlocal dispersive equations. Zbl 1218.35175
Liu, Hailiang; Yin, Zhaoyang
6
2010
Global regularity of the 4D restricted Euler equations. Zbl 1193.37123
Liu, Hailiang; Tadmor, Eitan; Wei, Dongming
6
2010
The direct discontinuous Galerkin (DDG) methods for diffusion problems. Zbl 1189.65227
Liu, Hailiang; Yan, Jue
69
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
8
2009
Critical thresholds in a relaxation system with resonance of characteristic speeds. Zbl 1171.35428
Li, Tong; Liu, Hailiang
3
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.
14
2008
On discreteness of the Hopf equation. Zbl 1149.65071
Liu, Hai-liang
9
2008
Robust control of robotic manipulators based on integral sliding mode. Zbl 1154.93344
Shi, J.; Liu, H.; Bajcinca, N.
6
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
A nonlocal conservation law with nonlinear “radiation” inhomogeneity. Zbl 1158.35063
di Francesco, Marco; Fellner, Klemens; Liu, Hailiang
5
2008
Global attractor for a nonlinear thermoviscoelastic system in shape memory alloys. Zbl 1173.35386
Qin, Yuming; Liu, Hailiang; Song, Changming
4
2008
Critical thresholds in a relaxation model for traffic flows. Zbl 1152.35006
Li, Tong; Liu, Hailiang
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
Surfaces in the lightlike cone. Zbl 1108.53011
Liu, H. L.
10
2007
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
24
2006
Wave breaking in a class of nonlocal dispersive wave equations. Zbl 1110.35069
Liu, Hailiang
22
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.
67
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
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.
33
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
24
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
6
2005
Semi-active fuzzy sliding mode control of full vehicle and suspensions. Zbl 1182.70067
Liu, H.; Nonami, K.; Hagiwara, T.
5
2005
Relaxation dynamics, scaling limits and convergence of relaxation schemes. Zbl 1094.35078
Liu, Hailiang
2
2005
Molecular dynamics simulations of polyampholytes inside a slit. Zbl 1074.82555
Feng, J.; Liu, H.; Hu, Y.
1
2005
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
77
2004
Rotation prevents finite-time breakdown. Zbl 1098.76643
Liu, Hailiang; Tadmor, Eitan
21
2004
KdV dynamics in the plasma-sheath transition. Zbl 1060.76137
Liu, Hailiang; Slemrod, M.
9
2004
Pattern formation, wave propagation and stability in conservation laws with slow diffusion and fast reaction. Zbl 1065.35156
Fan, Haitao; Liu, Hailiang
3
2004
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
157
2003
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
Critical thresholds in 2D restricted Euler-Poisson equations. Zbl 1073.35187
Liu, Hailiang; Tadmor, Eitan
27
2003
...and 36 more Documents
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Cited by 832 Authors

65 Liu, Hailiang
20 Yang, Hanchun
16 Shu, Chi-Wang
15 Shen, Chun
14 Huang, Yunqing
13 Sun, Meina
13 Zhang, Yu
12 Cheng, Hongjun
12 Jin, Shi
12 Yi, Nianyu
12 Yin, Gan
10 Wang, Zhongming
9 Shao, Zhiqiang
9 Yu, Xijun
8 Guo, Lihui
8 Huang, Chaobao
8 Yan, Jue
8 Zhang, Pingwen
7 An, Na
7 Lee, Yongki
7 Li, Tong
7 Nedeljkov, Marko
7 Pang, Yicheng
7 Tadmor, Eitan
7 Wang, Jinhuan
7 Xu, Yan
7 Zhang, Yanyan
6 Cheng, Jian
6 Degond, Pierre
6 Fox, Rodney O.
6 Liu, Tiegang
6 Meng, Xiong
6 Osher, Stanley Joel
6 Runborg, Olof
6 Sarrico, Carlos Orlando R.
6 Sheng, Wancheng
6 Wang, Wei
6 Yang, Xu
5 Carrillo de la Plata, José Antonio
5 Liu, Jinjing
5 Mitrovic, Darko
5 Qian, Jianliang
5 Süli, Endre E.
5 Tan, Changhui
5 Wen, Xin
5 Wu, Boying
5 Xing, Yulong
5 Zhang, Rongpei
5 Zhu, Changjiang
4 Baccouch, Mahboub
4 Barrett, John W.
4 Cheng, Yingda
4 Choi, Young-Pil
4 Dai, Limei
4 Gosse, Laurent
4 He, Dongdong
4 Motamed, Mohammad
4 Pan, Kejia
4 Pu, Xueke
4 Tao, Qi
4 Titi, Edriss Saleh
4 Tsai, Yen-Hsi Richard
4 Xia, Yinhua
4 Yin, Peimeng
4 Yong, Wen-An
4 Yuen, Manwai
4 Zhang, Dazhi
4 Zhang, Mengping
4 Zhang, Zhifei
4 Zhang, Zhiyue
4 Zhou, Hong
4 Zhou, Shenggao
4 Zhu, Jiang
3 Cao, Waixiang
3 Chen, Zheng
3 Cheng, Bin
3 Cheng, Yao
3 Cockburn, Bernardo
3 Dehghan Takht Fooladi, Mehdi
3 Du, Qiang
3 Gottlieb, Sigal
3 Huang, Hongying
3 Karlsen, Kenneth Hvistendahl
3 Klar, Axel
3 Kwon, Bongsuk
3 LeFloch, Philippe Gerard
3 Li, Shiwei
3 Li, Xianggui
3 Loula, Abimael Fernando Dourado
3 Lukáčová-Medvid’ová, Mária
3 Luo, Hong
3 Markowich, Peter Alexander
3 Mei, Ming
3 Mizerová, Hana
3 Natalini, Roberto
3 Nishikawa, Hiroaki
3 Qu, Aifang
3 Rohde, Christian
3 Rozanova, Olga S.
3 Ruan, Lizhi
...and 732 more Authors
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Cited in 140 Serials

78 Journal of Computational Physics
49 Journal of Scientific Computing
46 Journal of Differential Equations
33 Journal of Mathematical Analysis and Applications
21 Journal of Mathematical Physics
20 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods
19 M\(^3\)AS. Mathematical Models & Methods in Applied Sciences
16 Mathematics of Computation
16 Journal of Computational and Applied Mathematics
11 ZAMP. Zeitschrift für angewandte Mathematik und Physik
11 Physica D
11 Applied Numerical Mathematics
11 Journal of Hyperbolic Differential Equations
10 Archive for Rational Mechanics and Analysis
10 Computers & Mathematics with Applications
10 Communications on Pure and Applied Analysis
9 Computers and Fluids
9 Applied Mathematics and Computation
9 Numerische Mathematik
9 SIAM Journal on Numerical Analysis
9 Applied Mathematics Letters
8 Mathematical Methods in the Applied Sciences
8 SIAM Journal on Mathematical Analysis
8 Nonlinear Analysis. Real World Applications
8 Advances in Mathematical Physics
7 Acta Applicandae Mathematicae
7 SIAM Journal on Scientific Computing
6 Wave Motion
6 Chinese Annals of Mathematics. Series B
6 Numerical Algorithms
5 Applicable Analysis
5 Communications in Mathematical Physics
5 Computer Methods in Applied Mechanics and Engineering
5 Communications on Pure and Applied Mathematics
5 Abstract and Applied Analysis
5 Science China. Mathematics
4 SIAM Journal on Applied Mathematics
4 Physics of Fluids
4 Discrete and Continuous Dynamical Systems
4 Nonlinear Dynamics
4 European Journal of Mechanics. B. Fluids
4 Bulletin of the Malaysian Mathematical Sciences Society. Second Series
4 Boundary Value Problems
3 Nonlinearity
3 BIT
3 Monatshefte für Mathematik
3 Quarterly of Applied Mathematics
3 Numerical Methods for Partial Differential Equations
3 Applied Mathematical Modelling
3 Communications in Partial Differential Equations
3 International Journal of Computer Mathematics
3 Computational and Applied Mathematics
3 Advances in Computational Mathematics
3 Mathematical Problems in Engineering
3 Mathematics and Mechanics of Solids
3 Journal of Nonlinear Mathematical Physics
3 Multiscale Modeling & Simulation
3 European Series in Applied and Industrial Mathematics (ESAIM): Mathematical Modelling and Numerical Analysis
3 Kinetic and Related Models
3 Journal of Applied Analysis and Computation
2 Journal of Statistical Physics
2 Bulletin of Mathematical Biology
2 Advances in Mathematics
2 Annales de l’Institut Henri Poincaré. Analyse Non Linéaire
2 Computational Mathematics and Mathematical Physics
2 Proceedings of the Royal Society of Edinburgh. Section A. Mathematics
2 Applied and Computational Harmonic Analysis
2 ZAMM. Zeitschrift für Angewandte Mathematik und Mechanik
2 Journal of Mathematical Fluid Mechanics
2 Communications in Nonlinear Science and Numerical Simulation
2 Comptes Rendus. Mathématique. Académie des Sciences, Paris
2 Acta Numerica
2 Research in the Mathematical Sciences
2 Communications on Applied Mathematics and Computation
1 International Journal of General Systems
1 Indian Journal of Pure & Applied Mathematics
1 Journal of Engineering Mathematics
1 Journal of Mathematical Biology
1 Moscow University Mathematics Bulletin
1 Physics Letters. A
1 Rocky Mountain Journal of Mathematics
1 Theoretical and Mathematical Physics
1 Zhurnal Vychislitel’noĭ Matematiki i Matematicheskoĭ Fiziki
1 Journal of Geometry and Physics
1 Duke Mathematical Journal
1 International Journal for Numerical Methods in Engineering
1 Inventiones Mathematicae
1 Journal of Functional Analysis
1 Journal of the Korean Mathematical Society
1 Mathematics and Computers in Simulation
1 Pacific Journal of Mathematics
1 Proceedings of the American Mathematical Society
1 Proceedings of the Edinburgh Mathematical Society. Series II
1 Ricerche di Matematica
1 Transactions of the American Mathematical Society
1 Applied Mathematics and Mechanics. (English Edition)
1 Acta Mathematicae Applicatae Sinica. English Series
1 Mathematical and Computer Modelling
1 Asymptotic Analysis
1 Forum Mathematicum
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