Edit Profile (opens in new tab) Liu, Hailiang Co-Author Distance Author ID: liu.hailiang Published as: Liu, Hailiang; Liu, H.; Liu, Hai-liang more...less Homepage: https://faculty.sites.iastate.edu/hliu/ External Links: MGP · ORCID · Google Scholar · ResearchGate Documents Indexed: 172 Publications since 1992, including 13 Additional arXiv Preprints Co-Authors: 86 Co-Authors with 151 Joint Publications 3,099 Co-Co-Authors 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 all top 5 Fields 139 Partial differential equations (35-XX) 90 Numerical analysis (65-XX) 33 Fluid mechanics (76-XX) 17 Statistical mechanics, structure of matter (82-XX) 14 Biology and other natural sciences (92-XX) 11 Operations research, mathematical programming (90-XX) 7 Quantum theory (81-XX) 5 Dynamical systems and ergodic theory (37-XX) 5 Calculus of variations and optimal control; optimization (49-XX) 5 Optics, electromagnetic theory (78-XX) 4 Approximations and expansions (41-XX) 4 Computer science (68-XX) 3 Integral equations (45-XX) 2 Ordinary differential equations (34-XX) 2 Mechanics of deformable solids (74-XX) 2 Systems theory; control (93-XX) 1 Difference and functional equations (39-XX) 1 Global analysis, analysis on manifolds (58-XX) 1 Mechanics of particles and systems (70-XX) 1 Relativity and gravitational theory (83-XX) 1 Astronomy and astrophysics (85-XX) 1 Geophysics (86-XX) 1 Game theory, economics, finance, and other social and behavioral sciences (91-XX) Publications by Year all cited Publications top 5 cited Publications 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 all cited Publications top 5 cited Publications all top 5 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 all top 5 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. 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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 all top 5 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) Citations by Year