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Author ID: liu.hailiang Recent zbMATH articles by "Liu, Hailiang"
Published as: Liu, Hailiang; Liu, H.; Liu, Hai-liang
Homepage: https://faculty.sites.iastate.edu/hliu/
External Links: MGP · ORCID · Google Scholar · ResearchGate
all top 5

Co-Authors

21 single-authored
11 Yin, Peimeng
9 Wang, Jinghua
9 Wang, Zhongming
9 Yi, Nianyu
8 Bhatnagar, Manas
8 Huang, Yunqing
8 Tadmor, Eitan
8 Tian, Xuping
7 Warnecke, Gerald G.
6 Yu, Hui
5 Cai, Wenli
5 Li, Tong
5 Osher, Stanley Joel
4 Jiang, Yi
4 Jin, Shi
4 Maimaitiyiming, Wumaier
4 Ralston, James V.
4 Yang, Tong
3 Huo, Xiaokai
3 Jabin, Pierre-Emmanuel
3 Lee, Yongki
3 Pollack, Michael
3 Runborg, Olof
3 Shin, Jaemin
3 Tanushev, Nicolay M.
3 Tsai, Yen-Hsi Richard
3 Yan, Jue
2 Chen, Gui-Qiang G.
2 Cheng, Li-Tien
2 Degond, Pierre
2 Levermore, C. David
2 Lu, Wenying
2 Pan, Jun
2 Pego, Robert Leo
2 Pryporov, Maksym
2 Saran, Haseena
2 Wen, Hairui
2 Zhang, Hui
2 Zhang, Pingwen
1 Ballew, Joshua
1 Bressan, Alberto
1 Cao, Waixiang
1 Chen, Yaoyao
1 Di Francesco, Marco
1 Engelberg, Shlomo
1 Fan, Haitao
1 Fellner, Klemens
1 Feng, Xiaobing
1 Fox, Rodney O.
1 Ganapathysubramanian, Baskar
1 Gao, Hongyang
1 Gao, Tianxiang
1 Gröpler, Robin
1 Ha, Tae Gab
1 He, Jiahao
1 Iyer, Gautam
1 Kunik, Matthias
1 Liu, Chun
1 Liu, Jia
1 Ma, Shu
1 Markowich, Peter Alexander
1 Natalini, Roberto
1 Nurbekyan, Levon
1 Pendleton, Terrance
1 Ploymaklam, Nattapol
1 Qian, Linrui
1 Qin, Yuming
1 Rajan, Hridesh
1 Savelief, D.
1 Slemrod, Marshall
1 Song, Changming
1 Sparber, Christof
1 Su, Ning
1 Tan, Changhui
1 Thein, Ferdinand
1 Tzavaras, Athanasios E.
1 Vignal, Marie-Hélène
1 Wang, Lihe
1 Wang, Shuaikun
1 Wei, Dongming
1 Woo, Chingwah
1 Xing, Yulong
1 Yang, Yunan
1 Yin, Zhaoyang
1 Yong, Wen-An
1 Zhang, Zhimin
all top 5

Serials

21 Journal of Computational Physics
9 Journal of Differential Equations
8 Mathematics of Computation
8 Journal of Scientific Computing
8 Communications in Computational Physics
6 SIAM Journal on Numerical Analysis
6 Physica D
6 SIAM Journal on Mathematical Analysis
6 SIAM Journal on Scientific Computing
6 Communications in Mathematical Sciences
5 Applied Mathematics Letters
4 Journal of Computational and Applied Mathematics
4 Numerical Methods for Partial Differential Equations
4 M\(^3\)AS. Mathematical Models & Methods in Applied Sciences
4 Methods and Applications of Analysis
4 Discrete and Continuous Dynamical Systems
3 Numerische Mathematik
3 SIAM Journal on Applied Mathematics
3 Journal of Hyperbolic Differential Equations
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 Communications on Pure and Applied Analysis
2 Multiscale Modeling & Simulation
2 European Series in Applied and Industrial Mathematics (ESAIM): Mathematical Modelling and Numerical Analysis
1 Communications in Mathematical Physics
1 IMA Journal of Numerical Analysis
1 Journal of Mathematical Analysis and Applications
1 Nonlinearity
1 Transport Theory and Statistical Physics
1 Wave Motion
1 ZAMP. Zeitschrift für angewandte Mathematik und Physik
1 Acta Mathematicae Applicatae Sinica
1 Applied Numerical Mathematics
1 Acta Mathematicae Applicatae Sinica. English Series
1 Annals of Differential Equations
1 Asymptotic Analysis
1 Systems Science and Mathematical Sciences
1 Numerical Algorithms
1 Communications in Partial Differential Equations
1 Acta Mathematica Scientia
1 Journal of Partial Differential Equations
1 Journal of Nonlinear Mathematical Physics
1 Communications in Information and Systems
1 Networks and Heterogeneous Media
1 Annals of Applied Mathematics

Publications by Year

Citations contained in zbMATH Open

136 Publications have been cited 1,916 times in 1,064 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
230
2003
The direct discontinuous Galerkin (DDG) methods for diffusion problems. Zbl 1189.65227
Liu, Hailiang; Yan, Jue
115
2009
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
112
2004
The direct discontinuous Galerkin (DDG) method for diffusion with interface corrections. Zbl 1364.65200
Liu, Hailiang; Yan, Jue
78
2010
Critical thresholds in Euler-Poisson equations. Zbl 0989.35110
Engelberg, Shlomo; Liu, Hailiang; Tadmor, Eitan
71
2001
Spectral dynamics of the velocity gradient field in restricted flows. Zbl 1031.76006
Liu, Hailiang; Tadmor, Eitan
45
2002
A free energy satisfying finite difference method for Poisson-Nernst-Planck equations. Zbl 1349.65317
Liu, Hailiang; Wang, Zhongming
42
2014
Critical thresholds in a convolution model for nonlinear conservation laws. Zbl 1002.35085
Liu, Hailiang; Tadmor, Eitan
39
2001
Critical thresholds in 2D restricted Euler-Poisson equations. Zbl 1073.35187
Liu, Hailiang; Tadmor, Eitan
39
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
38
2003
A local discontinuous Galerkin method for the Korteweg-de Vries equation with boundary effect. Zbl 1092.65083
Liu, Hailiang; Yan, Jue
38
2006
Optimal error estimates of the direct discontinuous Galerkin method for convection-diffusion equations. Zbl 1331.65141
Liu, Hailiang
38
2015
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
36
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
36
2005
Rotation prevents finite-time breakdown. Zbl 1098.76643
Liu, Hailiang; Tadmor, Eitan
33
2004
A free energy satisfying discontinuous Galerkin method for one-dimensional Poisson-Nernst-Planck systems. Zbl 1406.82021
Liu, Hailiang; Wang, Zhongming
33
2017
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
31
2013
Superconvergence of the direct discontinuous Galerkin method for convection-diffusion equations. Zbl 1361.65061
Cao, Waixiang; Liu, Hailiang; Zhang, Zhimin
28
2017
Error estimates for Gaussian beam superpositions. Zbl 1277.35236
Liu, Hailiang; Runborg, Olof; Tanushev, Nicolay M.
26
2013
A Hamiltonian preserving discontinuous Galerkin method for the generalized Korteweg-de Vries equation. Zbl 1349.65462
Liu, Hailiang; Yi, Nianyu
25
2016
Wave breaking in a class of nonlocal dispersive wave equations. Zbl 1110.35069
Liu, Hailiang
23
2006
Mass preserving discontinuous Galerkin methods for Schrödinger equations. Zbl 1352.65358
Lu, Wenying; Huang, Yunqing; Liu, Hailiang
23
2015
Maximum-principle-satisfying third order discontinuous Galerkin schemes for Fokker-Planck equations. Zbl 1341.65038
Liu, Hailiang; Yu, Hui
23
2014
A local discontinuous Galerkin method for the Burgers-Poisson equation. Zbl 1339.65177
Liu, Hailiang; Ploymaklam, Nattapol
21
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
The entropy satisfying discontinuous Galerkin method for Fokker-Planck equations. Zbl 1320.65143
Liu, Hailiang; Yu, Hui
20
2015
Critical thresholds in hyperbolic relaxation systems. Zbl 1170.35062
Li, Tong; Liu, Hailiang
17
2009
An entropy satisfying discontinuous Galerkin method for nonlinear Fokker-Planck equations. Zbl 1354.35158
Liu, Hailiang; Wang, Zhongming
17
2016
Unconditionally energy stable DG schemes for the Swift-Hohenberg equation. Zbl 1427.65372
Liu, Hailiang; Yin, Peimeng
17
2019
An invariant preserving discontinuous Galerkin method for the Camassa-Holm equation. Zbl 1382.65321
Liu, Hailiang; Xing, Yulong
15
2016
Kinetic models for polymers with inertial effects. Zbl 1183.76614
Degond, Pierre; Liu, Hailiang
14
2009
Asymptotic stability of relaxation shock profiles for hyperbolic conservation laws. Zbl 1039.35063
Liu, Hailiang
14
2003
Thresholds for shock formation in traffic flow models with Arrhenius look-ahead dynamics. Zbl 1304.35420
Lee, Yongki; Liu, Hailiang
14
2015
Mass- and energy-conserved numerical schemes for nonlinear Schrödinger equations. Zbl 1473.65102
Feng, Xiaobing; Liu, Hailiang; Ma, Shu
14
2019
Multi-valued solution and level set methods in computational high frequency wave propagation. Zbl 1120.65110
Liu, H.; Osher, S.; Tsai, R.
13
2006
Recovery of high frequency wave fields from phase space-based measurements. Zbl 1221.35031
Liu, Hailiang; Ralston, James
13
2010
Stability of a relaxation model with a nonconvex flux. Zbl 0961.35017
Liu, Hailiang; Wang, Jinghua; Yang, Tong
13
1998
Recovery of normal derivatives from the piecewise \(L^2\) projection. Zbl 1408.65009
Huang, Yunqing; Liu, Hailiang; Yi, Nianyu
13
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.
13
2012
Critical thresholds in one-dimensional damped Euler-Poisson systems. Zbl 1453.35145
Bhatnagar, Manas; Liu, Hailiang
13
2020
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
12
2012
Efficient, positive, and energy stable schemes for multi-d Poisson-Nernst-Planck systems. Zbl 1471.35277
Liu, Hailiang; Maimaitiyiming, Wumaier
12
2021
Thresholds in three-dimensional restricted Euler-Poisson equations. Zbl 1434.35105
Lee, Yongki; Liu, Hailiang
12
2013
A mixed discontinuous Galerkin method without interior penalty for time-dependent fourth order problems. Zbl 1407.65168
Liu, Hailiang; Yin, Peimeng
12
2018
Convergence rates for relaxation schemes approximating conservation laws. Zbl 0954.35108
Liu, Hailiang; Warnecke, Gerald
11
2000
On discreteness of the Hopf equation. Zbl 1149.65071
Liu, Hai-liang
11
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
11
2018
KdV dynamics in the plasma-sheath transition. Zbl 1060.76137
Liu, Hailiang; Slemrod, M.
10
2004
Decay rate for travelling waves of a relaxation model. Zbl 0908.35074
Liu, Hailiang; Woo, Ching Wah; Yang, Tong
10
1997
Recovery of high frequency wave fields for the acoustic wave equation. Zbl 1213.35284
Liu, Hailiang; Ralston, James
9
2010
Stability of a traffic flow model with nonconvex relaxation. Zbl 1099.35156
Li, Tong; Liu, Hailiang
9
2005
The \(L^p\) stability of relaxation rarefaction profiles. Zbl 0988.35113
Liu, Hailiang
8
2001
Semiclassical limit of the nonlinear Schrödinger-Poisson equation with subcritical initial data. Zbl 1166.35374
Liu, Hailiang; Tadmor, Eitan
8
2002
A conservative discontinuous Galerkin method for the Degasperis-Procesi equation. Zbl 1296.35158
Huang, Yunqing; Liu, Hailiang; Yi, Nianyu
8
2014
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
8
2016
A nonlocal conservation law with nonlinear “radiation” inhomogeneity. Zbl 1158.35063
di Francesco, Marco; Fellner, Klemens; Liu, Hailiang
8
2008
Unconditional positivity-preserving and energy stable schemes for a reduced Poisson-Nernst-Planck system. Zbl 1473.65263
Liu, Hailiang; Maimaitiyiming, Wumaier
8
2020
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
Global regularity, and wave breaking phenomena in a class of nonlocal dispersive equations. Zbl 1218.35175
Liu, Hailiang; Yin, Zhaoyang
7
2010
Diffusion limit of a hyperbolic system with relaxation. Zbl 0922.35086
Jin, Shi; Liu, Hailiang
7
1998
Alternating evolution discontinuous Galerkin methods for Hamilton-Jacobi equations. Zbl 1349.65461
Liu, Hailiang; Pollack, Michael
7
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.
7
2016
Time-asymptotic convergence rates towards the discrete evolutionary stable distribution. Zbl 1328.65268
Cai, Wenli; Jabin, Pierre-Emmanuel; Liu, Hailiang
7
2015
Global regularity of the 4D restricted Euler equations. Zbl 1193.37123
Liu, Hailiang; Tadmor, Eitan; Wei, Dongming
7
2010
On accuracy of the mass-preserving DG method to multi-dimensional Schrödinger equations. Zbl 1461.65241
Liu, Hailiang; Huang, Yunqing; Lu, Wenying; Yi, Nianyu
7
2019
Global well-posedness for the microscopic FENE model with a sharp boundary condition. Zbl 1233.35109
Liu, Hailiang; Shin, Jaemin
6
2012
Threshold for shock formation in the hyperbolic Keller-Segel model. Zbl 1330.35250
Lee, Yongki; Liu, Hailiang
6
2015
An iterative discontinuous Galerkin method for solving the nonlinear Poisson Boltzmann equation. Zbl 1388.65162
Yin, Peimeng; Huang, Yunqing; Liu, Hailiang
6
2014
Critical thresholds in a relaxation model for traffic flows. Zbl 1152.35006
Li, Tong; Liu, Hailiang
6
2008
High order unconditionally energy stable RKDG schemes for the Swift-Hohenberg equation. Zbl 1491.65145
Liu, Hailiang; Yin, Peimeng
6
2022
An energy conserving local discontinuous Galerkin method for a nonlinear variational wave equation. Zbl 1488.65482
Yi, Nianyu; Liu, Hailiang
6
2018
Global orientation dynamics for liquid crystalline polymers. Zbl 1183.82101
Liu, Hailiang
5
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
Superposition of multi-valued solutions in high frequency wave dynamics. Zbl 1203.65141
Liu, Hailiang; Wang, Zhongming
5
2008
Alternating evolution schemes for hyperbolic conservation laws. Zbl 1248.65092
Saran, Haseena; Liu, Hailiang
5
2011
Long-time diffusive behavior of solutions to a hyperbolic relaxation system. Zbl 0981.35035
Liu, Hailiang; Natalini, Roberto
5
2001
Time-asymptotic stability of boundary-layers for a hyperbolic relaxation system. Zbl 0997.35007
Liu, Hailiang; Yong, Wen-An
5
2001
Gaussian beam methods for the Helmholtz equation. Zbl 1302.35135
Liu, Hailiang; Ralston, James; Runborg, Olof; Tanushev, Nicolay M.
5
2014
Alternating evolution discontinuous Galerkin methods for convection-diffusion equations. Zbl 1352.65356
Liu, Hailiang; Pollack, Michael
5
2016
Boundary conditions for the microscopic FENE models. Zbl 1147.76003
Liu, Chun; Liu, Hailiang
5
2008
On a non-local selection-mutation model with a gradient flow structure. Zbl 1382.35313
Jabin, Pierre-Emmanuel; Liu, Hailiang
5
2017
Entropy satisfying schemes for computing selection dynamics in competitive interactions. Zbl 1318.65085
Liu, Hailiang; Cai, Wenli; Su, Ning
5
2015
Unconditionally energy stable discontinuous Galerkin schemes for the Cahn-Hilliard equation. Zbl 1480.65264
Liu, Hailiang; Yin, Peimeng
5
2021
A conservative discontinuous Galerkin method for nonlinear electromagnetic Schrödinger equations. Zbl 1435.35364
Yi, Nianyu; Huang, Yunqing; Liu, Hailiang
5
2019
Positive and free energy satisfying schemes for diffusion with interaction potentials. Zbl 07507217
Liu, Hailiang; Maimaitiyiming, Wumaier
5
2020
Nonlinear stability and existence of stationary discrete travelling waves for the relaxing schemes. Zbl 0934.65101
Liu, Hailiang; Wang, Jinghua; Yang, Tong
4
1999
Critical thresholds in a relaxation system with resonance of characteristic speeds. Zbl 1171.35428
Li, Tong; Liu, Hailiang
4
2009
Critical thresholds in the semiclassical limit of 2D rotational Schrödinger equations. Zbl 1089.35052
Liu, Hailiang
4
2006
Global attractor for a nonlinear thermoviscoelastic system in shape memory alloys. Zbl 1173.35386
Qin, Yuming; Liu, Hailiang; Song, Changming
4
2008
Sobolev and max norm error estimates for Gaussian beam superpositions. Zbl 1372.35263
Liu, Hailiang; Runborg, Olof; Tanushev, Nicolay M.
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
An invariant-region-preserving limiter for DG schemes to isentropic Euler equations. Zbl 1416.76153
Jiang, Yi; Liu, Hailiang
4
2019
The lip\(^{+}\)-stability and error estimates for a relaxation scheme. Zbl 0980.35102
Liu, Hailiang; Wang, Jinghua; Warnecke, Gerald
3
2000
Asymptotic decay to relaxation shock fronts in two dimensions. Zbl 0994.35088
Liu, Hailiang
3
2001
Pattern formation, wave propagation and stability in conservation laws with slow diffusion and fast reaction. Zbl 1065.35156
Fan, Haitao; Liu, Hailiang
3
2004
Asymptotic stability of shock profiles for nonconvex convection-diffusion equation. Zbl 0888.35052
Liu, Hailiang
3
1997
On traveling wave solutions of the \(\theta\)-equation of dispersive type. Zbl 1304.35190
Ha, Tae Gab; Liu, Hailiang
3
2015
Oscillatory traveling wave solutions to an attractive chemotaxis system. Zbl 1350.35055
Li, Tong; Liu, Hailiang; Wang, Lihe
3
2016
A finite volume method for nonlocal competition-mutation equations with a gradient flow structure. Zbl 1378.92047
Cai, Wenli; Liu, Hailiang
3
2017
On the SAV-DG method for a class of fourth order gradient flows. Zbl 07776958
Liu, Hailiang; Yin, Peimeng
2
2023
A dynamic mass transport method for Poisson-Nernst-Planck equations. Zbl 07625383
Liu, Hailiang; Maimaitiyiming, Wumaier
2
2023
Critical thresholds in the Euler-Poisson-alignment system. Zbl 1527.35227
Bhatnagar, Manas; Liu, Hailiang; Tan, Changhui
1
2023
Global dynamics and photon loss in the Kompaneets equation. Zbl 1528.35207
Ballew, Joshua; Iyer, Gautam; Levermore, C. David; Liu, Hailiang; Pego, Robert L.
1
2023
High order unconditionally energy stable RKDG schemes for the Swift-Hohenberg equation. Zbl 1491.65145
Liu, Hailiang; Yin, Peimeng
6
2022
Positivity-preserving third order DG schemes for Poisson-Nernst-Planck equations. Zbl 07517725
Liu, Hailiang; Wang, Zhongming; Yin, Peimeng; Yu, Hui
2
2022
A mass- and energy-conserved DG method for the Schrödinger-Poisson equation. Zbl 1483.35230
Yi, Nianyu; Liu, Hailiang
1
2022
Efficient, positive, and energy stable schemes for multi-d Poisson-Nernst-Planck systems. Zbl 1471.35277
Liu, Hailiang; Maimaitiyiming, Wumaier
12
2021
Unconditionally energy stable discontinuous Galerkin schemes for the Cahn-Hilliard equation. Zbl 1480.65264
Liu, Hailiang; Yin, Peimeng
5
2021
Well-posedness and critical thresholds in a nonlocal Euler system with relaxation. Zbl 1486.35334
Bhatnagar, Manas; Liu, Hailiang
3
2021
Analysis of direct discontinuous Galerkin methods for multi-dimensional convection-diffusion equations. Zbl 1465.65100
Liu, Hailiang
2
2021
An energy stable and positivity-preserving scheme for the Maxwell-Stefan diffusion system. Zbl 1511.65083
Huo, Xiaokai; Liu, Hailiang; Tzavaras, Athanasios E.; Wang, Shuaikun
2
2021
Critical thresholds in one-dimensional damped Euler-Poisson systems. Zbl 1453.35145
Bhatnagar, Manas; Liu, Hailiang
13
2020
Unconditional positivity-preserving and energy stable schemes for a reduced Poisson-Nernst-Planck system. Zbl 1473.65263
Liu, Hailiang; Maimaitiyiming, Wumaier
8
2020
Positive and free energy satisfying schemes for diffusion with interaction potentials. Zbl 07507217
Liu, Hailiang; Maimaitiyiming, Wumaier
5
2020
Selection dynamics for deep neural networks. Zbl 1448.49029
Liu, Hailiang; Markowich, Peter
3
2020
Critical thresholds in 1D pressureless Euler-Poisson systems with variable background. Zbl 1490.35256
Bhatnagar, Manas; Liu, Hailiang
3
2020
General superpositions of Gaussian beams and propagation errors. Zbl 1429.35147
Liu, Hailiang; Ralston, James; Yin, Peimeng
1
2020
Unconditionally energy stable DG schemes for the Swift-Hohenberg equation. Zbl 1427.65372
Liu, Hailiang; Yin, Peimeng
17
2019
Mass- and energy-conserved numerical schemes for nonlinear Schrödinger equations. Zbl 1473.65102
Feng, Xiaobing; Liu, Hailiang; Ma, Shu
14
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
7
2019
A conservative discontinuous Galerkin method for nonlinear electromagnetic Schrödinger equations. Zbl 1435.35364
Yi, Nianyu; Huang, Yunqing; Liu, Hailiang
5
2019
Third order maximum-principle-satisfying DG schemes for convection-diffusion problems with anisotropic diffusivity. Zbl 1452.65260
Yu, Hui; Liu, Hailiang
4
2019
An invariant-region-preserving limiter for DG schemes to isentropic Euler equations. Zbl 1416.76153
Jiang, Yi; Liu, Hailiang
4
2019
A high order positivity preserving DG method for coagulation-fragmentation equations. Zbl 1426.65146
Liu, Hailiang; Gröpler, Robin; Warnecke, Gerald
3
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
12
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
11
2018
An energy conserving local discontinuous Galerkin method for a nonlinear variational wave equation. Zbl 1488.65482
Yi, Nianyu; 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
3
2018
Error estimates for the iterative discontinuous Galerkin method to the nonlinear Poisson-Boltzmann equation. Zbl 1488.65669
Yin, Peimeng; Huang, Yunqing; 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
A free energy satisfying discontinuous Galerkin method for one-dimensional Poisson-Nernst-Planck systems. Zbl 1406.82021
Liu, Hailiang; Wang, Zhongming
33
2017
Superconvergence of the direct discontinuous Galerkin method for convection-diffusion equations. Zbl 1361.65061
Cao, Waixiang; Liu, Hailiang; Zhang, Zhimin
28
2017
On a non-local selection-mutation model with a gradient flow structure. Zbl 1382.35313
Jabin, Pierre-Emmanuel; Liu, Hailiang
5
2017
A finite volume method for nonlocal competition-mutation equations with a gradient flow structure. Zbl 1378.92047
Cai, Wenli; Liu, Hailiang
3
2017
Error estimates for Gaussian beam methods applied to symmetric strictly hyperbolic systems. Zbl 1524.35368
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
25
2016
An entropy satisfying discontinuous Galerkin method for nonlinear Fokker-Planck equations. Zbl 1354.35158
Liu, Hailiang; Wang, Zhongming
17
2016
An invariant preserving discontinuous Galerkin method for the Camassa-Holm equation. Zbl 1382.65321
Liu, Hailiang; Xing, Yulong
15
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
8
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.
7
2016
Alternating evolution discontinuous Galerkin methods for convection-diffusion equations. Zbl 1352.65356
Liu, Hailiang; Pollack, Michael
5
2016
Sobolev and max norm error estimates for Gaussian beam superpositions. Zbl 1372.35263
Liu, Hailiang; Runborg, Olof; Tanushev, Nicolay M.
4
2016
Oscillatory traveling wave solutions to an attractive chemotaxis system. Zbl 1350.35055
Li, Tong; Liu, Hailiang; Wang, Lihe
3
2016
Optimal error estimates of the direct discontinuous Galerkin method for convection-diffusion equations. Zbl 1331.65141
Liu, Hailiang
38
2015
Mass preserving discontinuous Galerkin methods for Schrödinger equations. Zbl 1352.65358
Lu, Wenying; Huang, Yunqing; Liu, Hailiang
23
2015
A local discontinuous Galerkin method for the Burgers-Poisson equation. Zbl 1339.65177
Liu, Hailiang; Ploymaklam, Nattapol
21
2015
The entropy satisfying discontinuous Galerkin method for Fokker-Planck equations. Zbl 1320.65143
Liu, Hailiang; Yu, Hui
20
2015
Thresholds for shock formation in traffic flow models with Arrhenius look-ahead dynamics. Zbl 1304.35420
Lee, Yongki; Liu, Hailiang
14
2015
Time-asymptotic convergence rates towards the discrete evolutionary stable distribution. Zbl 1328.65268
Cai, Wenli; Jabin, Pierre-Emmanuel; Liu, Hailiang
7
2015
Threshold for shock formation in the hyperbolic Keller-Segel model. Zbl 1330.35250
Lee, Yongki; Liu, Hailiang
6
2015
Entropy satisfying schemes for computing selection dynamics in competitive interactions. Zbl 1318.65085
Liu, Hailiang; Cai, Wenli; Su, Ning
5
2015
On traveling wave solutions of the \(\theta\)-equation of dispersive type. Zbl 1304.35190
Ha, Tae Gab; Liu, Hailiang
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
42
2014
Maximum-principle-satisfying third order discontinuous Galerkin schemes for Fokker-Planck equations. Zbl 1341.65038
Liu, Hailiang; Yu, Hui
23
2014
A conservative discontinuous Galerkin method for the Degasperis-Procesi equation. Zbl 1296.35158
Huang, Yunqing; Liu, Hailiang; Yi, Nianyu
8
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
Gaussian beam methods for the Helmholtz equation. Zbl 1302.35135
Liu, Hailiang; Ralston, James; Runborg, Olof; Tanushev, Nicolay M.
5
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
31
2013
Error estimates for Gaussian beam superpositions. Zbl 1277.35236
Liu, Hailiang; Runborg, Olof; Tanushev, Nicolay M.
26
2013
Thresholds in three-dimensional restricted Euler-Poisson equations. Zbl 1434.35105
Lee, Yongki; Liu, Hailiang
12
2013
Alternating evolution schemes for Hamilton-Jacobi equations. Zbl 1270.65049
Liu, Hailiang; Pollack, Michael; Saran, Haseena
3
2013
Recovery of normal derivatives from the piecewise \(L^2\) projection. Zbl 1408.65009
Huang, Yunqing; Liu, Hailiang; Yi, Nianyu
13
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.
13
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
12
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
78
2010
Recovery of high frequency wave fields from phase space-based measurements. Zbl 1221.35031
Liu, Hailiang; Ralston, James
13
2010
Recovery of high frequency wave fields for the acoustic wave equation. Zbl 1213.35284
Liu, Hailiang; Ralston, James
9
2010
Global regularity, and wave breaking phenomena in a class of nonlocal dispersive equations. Zbl 1218.35175
Liu, Hailiang; Yin, Zhaoyang
7
2010
Global regularity of the 4D restricted Euler equations. Zbl 1193.37123
Liu, Hailiang; Tadmor, Eitan; Wei, Dongming
7
2010
The direct discontinuous Galerkin (DDG) methods for diffusion problems. Zbl 1189.65227
Liu, Hailiang; Yan, Jue
115
2009
Critical thresholds in hyperbolic relaxation systems. Zbl 1170.35062
Li, Tong; Liu, Hailiang
17
2009
Kinetic models for polymers with inertial effects. Zbl 1183.76614
Degond, Pierre; Liu, Hailiang
14
2009
Critical thresholds in a relaxation system with resonance of characteristic speeds. Zbl 1171.35428
Li, Tong; Liu, Hailiang
4
2009
On discreteness of the Hopf equation. Zbl 1149.65071
Liu, Hai-liang
11
2008
A nonlocal conservation law with nonlinear “radiation” inhomogeneity. Zbl 1158.35063
di Francesco, Marco; Fellner, Klemens; Liu, Hailiang
8
2008
Critical thresholds in a relaxation model for traffic flows. Zbl 1152.35006
Li, Tong; Liu, Hailiang
6
2008
Superposition of multi-valued solutions in high frequency wave dynamics. Zbl 1203.65141
Liu, Hailiang; Wang, Zhongming
5
2008
Boundary conditions for the microscopic FENE models. Zbl 1147.76003
Liu, Chun; 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
Rigorous derivation of the hydrodynamical equations for rotating superfluids. Zbl 1144.81462
Liu, Hailiang; Sparber, Christof
3
2008
An alternating evolution approximation to systems of hyperbolic conservation laws. Zbl 1162.35049
Liu, Hailiang
3
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
Global orientation dynamics for liquid crystalline polymers. Zbl 1183.82101
Liu, Hailiang
5
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
A local discontinuous Galerkin method for the Korteweg-de Vries equation with boundary effect. Zbl 1092.65083
Liu, Hailiang; Yan, Jue
38
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
...and 36 more Documents
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Cited by 1,282 Authors

85 Liu, Hailiang
27 Sun, Meina
26 Shen, Chun
23 Yang, Hanchun
20 Zhang, Yu
19 Shu, Chi-Wang
18 Yi, Nianyu
17 Huang, Yunqing
16 Liu, Tiegang
15 Cheng, Hongjun
15 Shao, Zhiqiang
14 Xu, Yan
13 Jin, Shi
13 Wang, Zhongming
13 Yin, Gan
12 Wang, Jinhuan
12 Yan, Jue
12 Zhang, Yanyan
11 Guo, Lihui
11 Pang, Yicheng
11 Tan, Changhui
10 Li, Tong
10 Zhang, Pingwen
10 Zhou, Shenggao
9 Baccouch, Mahboub
9 Choi, Young-Pil
9 Rozanova, Olga S.
9 Tadmor, Eitan
9 Yin, Peimeng
9 Yu, Xijun
8 Huang, Chaobao
8 Lee, Yongki
8 Meng, Xiong
8 Runborg, Olof
8 Xia, Yinhua
8 Xing, Yulong
7 An, Na
7 Cao, Waixiang
7 Carrillo de la Plata, José Antonio
7 Cheng, Jian
7 Cheng, Yingda
7 Degond, Pierre
7 Kim, Junseok
7 Nedeljkov, Marko
7 Osher, Stanley Joel
7 Qu, Aifang
7 Sheng, Wancheng
7 Tao, Qi
7 Wang, Wei
7 Wu, Boying
7 Yuan, Hairong
7 Zhang, Zhimin
6 Fox, Rodney O.
6 Li, Shiwei
6 Liu, Yong
6 Mitrovic, Darko
6 Sarrico, Carlos Orlando R.
6 Sekhar, T. Raja
6 Titi, Edriss Saleh
6 Tsai, Yen-Hsi Richard
6 Xu, Jie
6 Yang, Xu
6 Zhang, Fan
6 Zhang, Mengping
6 Zhu, Changjiang
5 Bhatnagar, Manas
5 Du, Qiang
5 Hong, John Meng-Kai
5 Lee, Hsin-Yi
5 Liang, Dong
5 Liu, Jinjing
5 Luo, Hong
5 Qian, Jianliang
5 Sheng, Shouqiong
5 Shu, Shi
5 Süli, Endre E.
5 Wei, Zhijian
5 Wen, Xin
5 Xu, Zhenli
5 Yan, Jinliang
5 Yong, Wen-An
5 Zhang, Qingling
5 Zhang, Rongpei
5 Zhang, Zhiyue
5 Zhou, Zhennan
4 Barrett, John William
4 Dai, Limei
4 Dehghan Takht Fooladi, Mehdi
4 Ding, Jie
4 Fu, Guosheng
4 Gosse, Laurent
4 He, Fen
4 Jung, Jinwook
4 Kwon, Bongsuk
4 Lasser, Caroline
4 Liu, Chun
4 Liu, Jianli
4 Lu, Benzhuo
4 Lukáčová-Medviďová, Mária
4 Ma, Shu
...and 1,182 more Authors
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Cited in 171 Serials

109 Journal of Computational Physics
67 Journal of Scientific Computing
57 Journal of Differential Equations
37 Journal of Mathematical Analysis and Applications
33 Journal of Mathematical Physics
29 Communications in Computational Physics
26 Journal of Computational and Applied Mathematics
22 M\(^3\)AS. Mathematical Models & Methods in Applied Sciences
21 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods
20 Physica D
18 ZAMP. Zeitschrift für angewandte Mathematik und Physik
17 Applied Numerical Mathematics
16 Computers & Mathematics with Applications
16 Mathematics of Computation
15 SIAM Journal on Numerical Analysis
14 SIAM Journal on Scientific Computing
14 Communications on Pure and Applied Analysis
13 Archive for Rational Mechanics and Analysis
13 Mathematical Methods in the Applied Sciences
13 SIAM Journal on Mathematical Analysis
13 Nonlinear Analysis. Real World Applications
12 Computers and Fluids
12 Applied Mathematics and Computation
12 Applied Mathematics Letters
12 Journal of Hyperbolic Differential Equations
11 Numerische Mathematik
11 Numerical Methods for Partial Differential Equations
10 Acta Applicandae Mathematicae
10 Numerical Algorithms
10 Computational and Applied Mathematics
10 Communications in Nonlinear Science and Numerical Simulation
10 Communications on Applied Mathematics and Computation
9 Boundary Value Problems
9 Advances in Applied Mathematics and Mechanics
8 Applicable Analysis
8 Quarterly of Applied Mathematics
8 Bulletin of the Malaysian Mathematical Sciences Society. Second Series
8 European Series in Applied and Industrial Mathematics (ESAIM): Mathematical Modelling and Numerical Analysis
8 Advances in Mathematical Physics
7 Nonlinearity
7 SIAM Journal on Applied Mathematics
7 ZAMM. Zeitschrift für Angewandte Mathematik und Mechanik
6 Computer Methods in Applied Mechanics and Engineering
6 Wave Motion
6 Chinese Annals of Mathematics. Series B
6 Advances in Computational Mathematics
6 Science China. Mathematics
5 Communications in Mathematical Physics
5 Communications on Pure and Applied Mathematics
5 BIT
5 Discrete and Continuous Dynamical Systems
5 Abstract and Applied Analysis
5 Journal of Mathematical Fluid Mechanics
5 Acta Numerica
5 Open Mathematics
4 Calcolo
4 Monatshefte für Mathematik
4 Asymptotic Analysis
4 Applied Mathematical Modelling
4 Physics of Fluids
4 Nonlinear Dynamics
4 European Journal of Mechanics. B. Fluids
4 International Journal of Nonlinear Sciences and Numerical Simulation
4 Kinetic and Related Models
4 Journal of Applied Analysis and Computation
3 Journal of Statistical Physics
3 Rocky Mountain Journal of Mathematics
3 Advances in Mathematics
3 Mathematics and Computers in Simulation
3 Ricerche di Matematica
3 Annales de l’Institut Henri Poincaré. Analyse Non Linéaire
3 Computational Mathematics and Mathematical Physics
3 Communications in Partial Differential Equations
3 International Journal of Computer Mathematics
3 Journal de Mathématiques Pures et Appliquées. Neuvième Série
3 Proceedings of the Royal Society of Edinburgh. Section A. Mathematics
3 Mathematical Problems in Engineering
3 Mathematics and Mechanics of Solids
3 Journal of Nonlinear Mathematical Physics
3 Multiscale Modeling & Simulation
3 Research in the Mathematical Sciences
2 Computer Physics Communications
2 Journal of Engineering Mathematics
2 Bulletin of Mathematical Biology
2 International Journal for Numerical Methods in Engineering
2 Journal of Functional Analysis
2 Journal of Computational Mathematics
2 Acta Mathematicae Applicatae Sinica. English Series
2 International Journal of Mathematics
2 SIAM Review
2 Journal of Dynamics and Differential Equations
2 Applied and Computational Harmonic Analysis
2 Journal of the European Mathematical Society (JEMS)
2 Journal of Evolution Equations
2 Discrete and Continuous Dynamical Systems. Series B
2 Computational Methods in Applied Mathematics
2 Acta Mathematica Scientia. Series B. (English Edition)
2 Comptes Rendus. Mathématique. Académie des Sciences, Paris
2 Journal of Applied Mathematics and Computing
2 Thai Journal of Mathematics
...and 71 more Serials
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Cited in 37 Fields

817 Partial differential equations (35-XX)
496 Numerical analysis (65-XX)
398 Fluid mechanics (76-XX)
97 Statistical mechanics, structure of matter (82-XX)
56 Biology and other natural sciences (92-XX)
44 Optics, electromagnetic theory (78-XX)
28 Quantum theory (81-XX)
26 Mechanics of deformable solids (74-XX)
24 Dynamical systems and ergodic theory (37-XX)
21 Operations research, mathematical programming (90-XX)
20 Ordinary differential equations (34-XX)
16 Functional analysis (46-XX)
15 Calculus of variations and optimal control; optimization (49-XX)
14 Geophysics (86-XX)
12 Relativity and gravitational theory (83-XX)
11 Integral equations (45-XX)
11 Probability theory and stochastic processes (60-XX)
10 Astronomy and astrophysics (85-XX)
9 Approximations and expansions (41-XX)
7 Mechanics of particles and systems (70-XX)
6 Real functions (26-XX)
6 Systems theory; control (93-XX)
5 Harmonic analysis on Euclidean spaces (42-XX)
5 Global analysis, analysis on manifolds (58-XX)
4 Computer science (68-XX)
4 Classical thermodynamics, heat transfer (80-XX)
4 Game theory, economics, finance, and other social and behavioral sciences (91-XX)
3 Linear and multilinear algebra; matrix theory (15-XX)
2 Measure and integration (28-XX)
2 Operator theory (47-XX)
1 General and overarching topics; collections (00-XX)
1 History and biography (01-XX)
1 Mathematical logic and foundations (03-XX)
1 Topological groups, Lie groups (22-XX)
1 Special functions (33-XX)
1 Difference and functional equations (39-XX)
1 Integral transforms, operational calculus (44-XX)

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