Edit Profile (opens in new tab) Liu, Hailiang Compute Distance To: Compute Author ID: liu.hailiang Published as: Liu, Hailiang; Liu, H.; Liu, Hai-liang Documents Indexed: 202 Publications since 1976 3 Further Contributions Co-Authors: 72 Co-Authors with 130 Joint Publications 2,889 Co-Co-Authors all top 5 Co-Authors 23 single-authored 9 Wang, Jinghua 9 Wang, Zhongming 8 Huang, Yunqing 8 Tadmor, Eitan 8 Yi, Nianyu 8 Yin, Peimeng 6 Warnecke, Gerald G. 6 Yu, Hui 5 Bhatnagar, Manas 5 Cai, Wenli 5 Li, Tong 5 Osher, Stanley Joel 4 Jiang, Yi 4 Jin, Shi 4 Ralston, James V. 4 Yang, Tong 3 Jabin, Pierre-Emmanuel 3 Lee, Yongki 3 Maimaitiyiming, Wumaier 3 Pollack, Michael 3 Runborg, Olof 3 Shin, Jaemin 3 Tanushev, Nicolay M. 3 Tsai, Yen-Hsi Richard 3 Yan, Jue 2 Bernussou, Jacques 2 Chen, Gui-Qiang G. 2 Cheng, Li-Tien 2 Degond, Pierre 2 Hadji, Layachi 2 Himeno, Ryutaro 2 Krishnan, Sreedevi 2 Lu, Wenying 2 Marella, Saikrishna V. 2 Pan, Jun 2 Pryporov, Maksym 2 Saran, Haseena 2 Schreiber, Willard C. 2 Shyy, Wei 2 Udaykumar, Holavanahalli S. 2 Wen, Hairui 2 Yamaguchi, Takami 1 Akulichev, Victor A. 1 Aten, Charlotte 1 Ates, Muzaffer 1 Axhausen, Kay W. 1 Ayachi, B. 1 Bajcinca, Naim 1 Barthès-Biesel, Dominique 1 Bathe, Klaus-Jürgen 1 Bau, E. 1 Bazargan-Sabet, B. 1 Borhan, Ali 1 Bressan, Alberto 1 Butterfaß, J. 1 Cao, Waixiang 1 Cesnik, Carlos E. S. 1 Chanchole, S. 1 Chui, E. 1 Cleary, Michael P. 1 Davulcu, Hasan 1 Desai, Chandra S. 1 Di Francesco, Marco 1 Dirr, Bodo 1 Engelberg, Shlomo 1 Fan, Haitao 1 Fan, Yuanxun 1 Fellner, Klemens 1 Feng, Xiaobing 1 Fox, Rodney O. 1 Garg, Hari Krishna 1 Gröpler, Robin 1 Gupta, N. R. 1 Ha, Tae Gab 1 Huang, Yuxia 1 Huo, Xiaokai 1 Ifju, Peter G. 1 Ikehata, Masaru 1 Iosevich, Alex 1 Jackiewicz, Zdzislaw 1 Katz, Casimir 1 Knoch, S. 1 Kobayashi, Shoichi 1 Kolippakkam, D. 1 Kuang, Yang 1 Lebon, Frédéric 1 Levermore, C. David 1 Li, Bingtuan 1 Lian, Yongsheng 1 Liang, Fugang 1 Liao, Guojun 1 Lien, Fue-Sang 1 Liu, Chun 1 Lott, Adam 1 Ma, Shu 1 MacKinnon, I. 1 Maimon, Shir 1 Markowich, Peter Alexander 1 McCartney, C. J. 1 Mehl, Michael J. ...and 58 more Co-Authors all top 5 Serials 24 Journal of Computational Physics 8 Mathematics of Computation 8 Journal of Differential Equations 8 Journal of Scientific Computing 8 Communications in Computational Physics 6 SIAM Journal on Numerical Analysis 6 Physica D 6 Applied Mathematics Letters 6 SIAM Journal on Scientific Computing 6 Communications in Mathematical Sciences 5 SIAM Journal on Mathematical Analysis 4 Journal of Computational and Applied Mathematics 4 M\(^3\)AS. Mathematical Models & Methods in Applied Sciences 4 Discrete and Continuous Dynamical Systems 3 International Journal for Numerical Methods in Fluids 3 International Journal of Solids and Structures 3 Numerische Mathematik 3 Numerical Methods for Partial Differential Equations 3 SIAM Journal on Applied Mathematics 3 Methods and Applications of Analysis 3 Journal of Hyperbolic Differential Equations 2 Computers and Structures 2 Molecular Simulation 2 Indiana University Mathematics Journal 2 Japan Journal of Industrial and Applied Mathematics 2 Proceedings of the Royal Society of Edinburgh. Section A. Mathematics 2 Multiscale Modeling & Simulation 2 European Series in Applied and Industrial Mathematics (ESAIM): Mathematical Modelling and Numerical Analysis 2 Advances and Applications in Fluid Mechanics 1 Communications in Mathematical Physics 1 Computer Methods in Applied Mechanics and Engineering 1 IMA Journal of Numerical Analysis 1 International Journal of Control 1 International Journal of Non-Linear Mechanics 1 International Journal of Systems Science 1 Journal of Fluid Mechanics 1 Journal of Mathematical Analysis and Applications 1 Journal of Sound and Vibration 1 Mathematical Notes 1 Nonlinearity 1 Transport Theory and Statistical Physics 1 Wave Motion 1 ZAMP. Zeitschrift für angewandte Mathematik und Physik 1 Zeitschrift für Angewandte Mathematik und Mechanik (ZAMM) 1 Fuzzy Sets and Systems 1 International Journal for Numerical Methods in Engineering 1 Journal of Functional Analysis 1 Mathematics and Computers in Simulation 1 Mechanics Research Communications 1 Mathematica Numerica Sinica 1 Acta Mathematicae Applicatae Sinica 1 Circuits, Systems, and Signal Processing 1 Acta Mathematica Hungarica 1 Parallel Computing 1 Applied Numerical Mathematics 1 Acta Mathematicae Applicatae Sinica. English Series 1 Annals of Differential Equations 1 Asymptotic Analysis 1 Signal Processing 1 Systems Science and Mathematical Sciences 1 Numerical Algorithms 1 Communications in Partial Differential Equations 1 Communications in Statistics. Simulation and Computation 1 Acta Mathematica Scientia 1 Journal of Partial Differential Equations 1 Advances in Engineering Software 1 Applied Mathematics. Series A (Chinese Edition) 1 Acustica - Acta Acustica 1 Journal of Vibration and Control 1 Wuhan University Journal of Natural Sciences (WUJNS) 1 Mechanism and Machine Theory 1 Flow, Turbulence and Combustion 1 Journal of Nonlinear Mathematical Physics 1 Communications in Information and Systems 1 Quantum Information Processing 1 Journal of Cosmology and Astroparticle Physics 1 Iranian Journal of Fuzzy Systems 1 Acta Mechanica Sinica 1 Networks and Heterogeneous Media 1 Quantum Studies: Mathematics and Foundations all top 5 Fields 133 Partial differential equations (35-XX) 89 Numerical analysis (65-XX) 47 Fluid mechanics (76-XX) 21 Statistical mechanics, structure of matter (82-XX) 18 Biology and other natural sciences (92-XX) 15 Mechanics of deformable solids (74-XX) 7 Quantum theory (81-XX) 5 Dynamical systems and ergodic theory (37-XX) 5 Mechanics of particles and systems (70-XX) 5 Optics, electromagnetic theory (78-XX) 5 Operations research, mathematical programming (90-XX) 4 Ordinary differential equations (34-XX) 4 Approximations and expansions (41-XX) 4 Calculus of variations and optimal control; optimization (49-XX) 4 Systems theory; control (93-XX) 3 Integral equations (45-XX) 3 Computer science (68-XX) 3 Geophysics (86-XX) 3 Information and communication theory, circuits (94-XX) 2 Group theory and generalizations (20-XX) 2 Difference and functional equations (39-XX) 2 Convex and discrete geometry (52-XX) 2 Global analysis, analysis on manifolds (58-XX) 2 Statistics (62-XX) 2 Classical thermodynamics, heat transfer (80-XX) 1 General and overarching topics; collections (00-XX) 1 Combinatorics (05-XX) 1 Order, lattices, ordered algebraic structures (06-XX) 1 Number theory (11-XX) 1 Abstract harmonic analysis (43-XX) 1 Relativity and gravitational theory (83-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 148 Publications have been cited 1,790 times in 806 Documents Cited by ▼ Year ▼ Formation of \(\delta\)-shocks and vacuum states in the vanishing pressure limit of solutions to the Euler equations for isentropic fluids. Zbl 1038.35035Chen, Gui-Qiang; Liu, Hailiang 176 2003 Concentration and cavitation in the vanishing pressure limit of solutions to the Euler equations for nonisentropic fluids. Zbl 1098.76603Chen, Gui-Qiang; Liu, Hailiang 87 2004 The direct discontinuous Galerkin (DDG) methods for diffusion problems. Zbl 1189.65227Liu, Hailiang; Yan, Jue 85 2009 Sharp interface Cartesian grid method. I: An easily implemented technique for 3D moving boundary computations. Zbl 1154.76359Marella, S.; Krishnan, S.; Liu, H.; Udaykumar, H. S. 72 2005 The direct discontinuous Galerkin (DDG) method for diffusion with interface corrections. Zbl 1364.65200Liu, Hailiang; Yan, Jue 68 2010 Critical thresholds in Euler-Poisson equations. Zbl 0989.35110Engelberg, Shlomo; Liu, Hailiang; Tadmor, Eitan 56 2001 Critical thresholds in a convolution model for nonlinear conservation laws. Zbl 1002.35085Liu, Hailiang; Tadmor, Eitan 38 2001 Computational high-frequency wave propagation using the level set method with applications to the semi-classical limit of Schrödinger equations. Zbl 1084.35066Cheng, Li-Tien; Liu, Hailiang; Osher, Stanley 37 2003 Spectral dynamics of the velocity gradient field in restricted flows. Zbl 1031.76006Liu, Hailiang; Tadmor, Eitan 37 2002 A numerical study of insect flight. Zbl 0929.76092Liu, H.; Kawachi, K. 35 1998 Modeling and simulation of capsules and biological cells. Zbl 1026.92002 35 2003 Effect of initial stress on the propagation behavior of Love waves in a layered piezoelectric structure. Zbl 1005.74033Liu, H.; Wang, Z. K.; Wang, T. J. 35 2001 Sharp interface Cartesian grid method. II: A technique for simulating droplet interactions with surfaces of arbitrary shape. Zbl 1154.76358Liu, H.; Krishnan, S.; Marella, S.; Udaykumar, H. S. 35 2005 Computing multivalued physical observables for the semiclassical limit of the Schrödinger equation. Zbl 1072.65132Jin, Shi; Liu, Hailiang; Osher, Stanley; Tsai, Yen-Hsi Richard 35 2005 A free energy satisfying finite difference method for Poisson-Nernst-Planck equations. Zbl 1349.65317Liu, Hailiang; Wang, Zhongming 33 2014 Optimal error estimates of the direct discontinuous Galerkin method for convection-diffusion equations. Zbl 1331.65141Liu, Hailiang 30 2015 Critical thresholds in 2D restricted Euler-Poisson equations. Zbl 1073.35187Liu, Hailiang; Tadmor, Eitan 30 2003 A numerical study of undulatory swimming. Zbl 0958.76099Liu, H.; Kawachi, K. 29 1999 A local discontinuous Galerkin method for the Korteweg-de Vries equation with boundary effect. Zbl 1092.65083Liu, Hailiang; Yan, Jue 26 2006 Axial symmetry and classification of stationary solutions of Doi-Onsager equation on the sphere with Maier-Saupe potential. Zbl 1092.76007Liu, Hailiang; Zhang, Hui; Zhang, Pingwen 26 2005 A direct discontinuous Galerkin method for the generalized Korteweg-de Vries equation: energy conservation and boundary effect. Zbl 1297.65122Yi, Nianyu; Huang, Yunqing; Liu, Hailiang 25 2013 Rotation prevents finite-time breakdown. Zbl 1098.76643Liu, Hailiang; Tadmor, Eitan 24 2004 Wave breaking in a class of nonlocal dispersive wave equations. Zbl 1110.35069Liu, Hailiang 23 2006 Superconvergence of the direct discontinuous Galerkin method for convection-diffusion equations. Zbl 1361.65061Cao, Waixiang; Liu, Hailiang; Zhang, Zhimin 22 2017 Error estimates for Gaussian beam superpositions. Zbl 1277.35236Liu, Hailiang; Runborg, Olof; Tanushev, Nicolay M. 21 2013 A free energy satisfying discontinuous Galerkin method for one-dimensional Poisson-Nernst-Planck systems. Zbl 1406.82021Liu, Hailiang; Wang, Zhongming 20 2017 Mass preserving discontinuous Galerkin methods for Schrödinger equations. Zbl 1352.65358Lu, Wenying; Huang, Yunqing; Liu, Hailiang 20 2015 Computing multi-valued physical observables for the high frequency limit of symmetric hyperbolic systems. Zbl 1098.65094Jin, Shi; Liu, Hailiang; Osher, Stanley; Tsai, Richard 20 2005 Maximum-principle-satisfying third order discontinuous Galerkin schemes for Fokker-Planck equations. Zbl 1341.65038Liu, Hailiang; Yu, Hui 18 2014 A local discontinuous Galerkin method for the Burgers-Poisson equation. Zbl 1339.65177Liu, Hailiang; Ploymaklam, Nattapol 18 2015 The entropy satisfying discontinuous Galerkin method for Fokker-Planck equations. Zbl 1320.65143Liu, Hailiang; Yu, Hui 17 2015 A Hamiltonian preserving discontinuous Galerkin method for the generalized Korteweg-de Vries equation. Zbl 1349.65462Liu, Hailiang; Yi, Nianyu 15 2016 Computational aerodynamics of low Reynolds number plunging, pitching and flexible wings for MAV applications. Zbl 1271.76285Shyy, W.; Lian, Y.; Tang, J.; Liu, H.; Trizila, P.; Stanford, B.; Bernal, L.; Cesnik, C.; Friedmann, P.; Ifju, P. 15 2008 Entropy-based fuzzy clustering and fuzzy modeling. Zbl 1147.62348Yao, J.; Dash, M.; Tan, S. T.; Liu, H. 14 2000 Asymptotic stability of relaxation shock profiles for hyperbolic conservation laws. Zbl 1039.35063Liu, Hailiang 14 2003 An entropy satisfying discontinuous Galerkin method for nonlinear Fokker-Planck equations. Zbl 1354.35158Liu, Hailiang; Wang, Zhongming 14 2016 Multi-valued solution and level set methods in computational high frequency wave propagation. Zbl 1120.65110Liu, H.; Osher, S.; Tsai, R. 13 2006 Stability of a relaxation model with a nonconvex flux. Zbl 0961.35017Liu, Hailiang; Wang, Jinghua; Yang, Tong 12 1998 Recovery of normal derivatives from the piecewise \(L^2\) projection. Zbl 1408.65009Huang, Yunqing; Liu, Hailiang; Yi, Nianyu 12 2012 Kinetic models for polymers with inertial effects. Zbl 1183.76614Degond, Pierre; Liu, Hailiang 12 2009 Recovery of high frequency wave fields from phase space-based measurements. Zbl 1221.35031Liu, Hailiang; Ralston, James 12 2010 Thresholds for shock formation in traffic flow models with Arrhenius look-ahead dynamics. Zbl 1304.35420Lee, Yongki; Liu, Hailiang 11 2015 Convergence rates for relaxation schemes approximating conservation laws. Zbl 0954.35108Liu, Hailiang; Warnecke, Gerald 10 2000 A note on harmonic maps. Zbl 0996.58507Liu, H.; Liao, Guojun 10 1996 Decay rate for travelling waves of a relaxation model. Zbl 0908.35074Liu, Hailiang; Woo, Ching Wah; Yang, Tong 10 1997 On discreteness of the Hopf equation. Zbl 1149.65071Liu, Hai-liang 10 2008 KdV dynamics in the plasma-sheath transition. Zbl 1060.76137Liu, Hailiang; Slemrod, M. 9 2004 An entropy satisfying conservative method for the Fokker-Planck equation of the finitely extensible nonlinear elastic dumbbell model. Zbl 1422.74097Liu, Hailiang; Yu, Hui 9 2012 Critical thresholds in hyperbolic relaxation systems. Zbl 1170.35062Li, Tong; Liu, Hailiang 9 2009 Unconditionally energy stable DG schemes for the Swift-Hohenberg equation. Zbl 1427.65372Liu, Hailiang; Yin, Peimeng 9 2019 An invariant preserving discontinuous Galerkin method for the Camassa-Holm equation. Zbl 1382.65321Liu, Hailiang; Xing, Yulong 9 2016 Numerical approximation of the Euler-Poisson-Boltzmann model in the quasineutral limit. Zbl 1395.76047Degond, P.; Liu, H.; Savelief, D.; Vignal, M.-H. 8 2012 A mixed discontinuous Galerkin method without interior penalty for time-dependent fourth order problems. Zbl 1407.65168Liu, Hailiang; Yin, Peimeng 8 2018 The \(L^p\) stability of relaxation rarefaction profiles. Zbl 0988.35113Liu, Hailiang 8 2001 Recovery of high frequency wave fields for the acoustic wave equation. Zbl 1213.35284Liu, Hailiang; Ralston, James 8 2010 Global regularity of the 4D restricted Euler equations. Zbl 1193.37123Liu, Hailiang; Tadmor, Eitan; Wei, Dongming 7 2010 Alternating evolution discontinuous Galerkin methods for Hamilton-Jacobi equations. Zbl 1349.65461Liu, Hailiang; Pollack, Michael 7 2014 Stability of a traffic flow model with nonconvex relaxation. Zbl 1099.35156Li, Tong; Liu, Hailiang 7 2005 A level set framework for capturing multi-valued solutions of nonlinear first-order equations. Zbl 1109.65080Liu, Hailiang; Cheng, Li-Tien; Osher, Stanley 7 2006 Diffusion limit of a hyperbolic system with relaxation. Zbl 0922.35086Jin, Shi; Liu, Hailiang 6 1998 Global regularity, and wave breaking phenomena in a class of nonlocal dispersive equations. Zbl 1218.35175Liu, Hailiang; Yin, Zhaoyang 6 2010 Global well-posedness for the microscopic FENE model with a sharp boundary condition. Zbl 1233.35109Liu, Hailiang; Shin, Jaemin 6 2012 Semiclassical limit of the nonlinear Schrödinger-Poisson equation with subcritical initial data. Zbl 1166.35374Liu, Hailiang; Tadmor, Eitan 6 2002 Robust control of robotic manipulators based on integral sliding mode. Zbl 1154.93344Shi, J.; Liu, H.; Bajcinca, N. 6 2008 Invariant-region-preserving DG methods for multi-dimensional hyperbolic conservation law systems, with an application to compressible Euler equations. Zbl 1416.65293Jiang, Yi; Liu, Hailiang 6 2018 An iterative discontinuous Galerkin method for solving the nonlinear Poisson Boltzmann equation. Zbl 1388.65162Yin, Peimeng; Huang, Yunqing; Liu, Hailiang 6 2014 Computing multi-valued velocity and electric fields for 1D Euler-Poisson equations. Zbl 1146.78012Liu, Hailiang; Wang, Zhongming 5 2007 A field-space-based level set method for computing multi-valued solutions to 1D Euler-Poisson equations. Zbl 1140.81399Liu, Hailiang; Wang, Zhongming 5 2007 Alternating evolution discontinuous Galerkin methods for convection-diffusion equations. Zbl 1352.65356Liu, Hailiang; Pollack, Michael 5 2016 Alternating evolution schemes for hyperbolic conservation laws. Zbl 1248.65092Saran, Haseena; Liu, Hailiang 5 2011 Critical thresholds in a relaxation model for traffic flows. Zbl 1152.35006Li, Tong; Liu, Hailiang 5 2008 A nonlocal conservation law with nonlinear “radiation” inhomogeneity. Zbl 1158.35063di Francesco, Marco; Fellner, Klemens; Liu, Hailiang 5 2008 Boundary conditions for the microscopic FENE models. Zbl 1147.76003Liu, Chun; Liu, Hailiang 5 2008 Semi-active fuzzy sliding mode control of full vehicle and suspensions. Zbl 1182.70067Liu, H.; Nonami, K.; Hagiwara, T. 5 2005 Tiling sets and spectral sets over finite fields. Zbl 1376.52038Aten, C.; Ayachi, B.; Bau, E.; FitzPatrick, D.; Iosevich, A.; Liu, H.; Lott, A.; MacKinnon, I.; Maimon, S.; Nan, S.; Pakianathan, J.; Petridis, G.; Rojas Mena, C.; Sheikh, A.; Tribone, T.; Weill, J.; Yu, C. 5 2017 Superposition of multi-valued solutions in high frequency wave dynamics. Zbl 1203.65141Liu, Hailiang; Wang, Zhongming 5 2008 On invariant-preserving finite difference schemes for the Camassa-Holm equation and the two-component Camassa-Holm system. Zbl 1388.65059Liu, Hailiang; Pendleton, Terrance 5 2016 Critical thresholds in one-dimensional damped Euler-Poisson systems. Zbl 1453.35145Bhatnagar, Manas; Liu, Hailiang 5 2020 Efficient, positive, and energy stable schemes for multi-d Poisson-Nernst-Planck systems. Zbl 1471.35277Liu, Hailiang; Maimaitiyiming, Wumaier 5 2021 Nonlinear stability and existence of stationary discrete travelling waves for the relaxing schemes. Zbl 0934.65101Liu, Hailiang; Wang, Jinghua; Yang, Tong 4 1999 Global orientation dynamics for liquid crystalline polymers. Zbl 1183.82101Liu, Hailiang 4 2007 A conservative discontinuous Galerkin method for the Degasperis-Procesi equation. Zbl 1296.35158Huang, Yunqing; Liu, Hailiang; Yi, Nianyu 4 2014 Gaussian beam methods for the Helmholtz equation. Zbl 1302.35135Liu, Hailiang; Ralston, James; Runborg, Olof; Tanushev, Nicolay M. 4 2014 Long-time diffusive behavior of solutions to a hyperbolic relaxation system. Zbl 0981.35035Liu, Hailiang; Natalini, Roberto 4 2001 Time-asymptotic stability of boundary-layers for a hyperbolic relaxation system. Zbl 0997.35007Liu, Hailiang; Yong, Wen-An 4 2001 Critical thresholds in the semiclassical limit of 2D rotational Schrödinger equations. Zbl 1089.35052Liu, Hailiang 4 2006 Critical thresholds in a relaxation system with resonance of characteristic speeds. Zbl 1171.35428Li, Tong; Liu, Hailiang 4 2009 Global attractor for a nonlinear thermoviscoelastic system in shape memory alloys. Zbl 1173.35386Qin, Yuming; Liu, Hailiang; Song, Changming 4 2008 A conservative discontinuous Galerkin method for nonlinear electromagnetic Schrödinger equations. Zbl 1435.35364Yi, Nianyu; Huang, Yunqing; Liu, Hailiang 4 2019 Thresholds in three-dimensional restricted Euler-Poisson equations. Zbl 1434.35105Lee, Yongki; Liu, Hailiang 4 2013 Time-asymptotic convergence rates towards the discrete evolutionary stable distribution. Zbl 1328.65268Cai, Wenli; Jabin, Pierre-Emmanuel; Liu, Hailiang 4 2015 Threshold for shock formation in the hyperbolic Keller-Segel model. Zbl 1330.35250Lee, Yongki; Liu, Hailiang 4 2015 Global dynamics of Bose-Einstein condensation for a model of the Kompaneets equation. Zbl 1362.37161Levermore, C. David; Liu, Hailiang; Pego, Robert L. 4 2016 Third order maximum-principle-satisfying DG schemes for convection-diffusion problems with anisotropic diffusivity. Zbl 1452.65260Yu, Hui; Liu, Hailiang 4 2019 On accuracy of the mass-preserving DG method to multi-dimensional Schrödinger equations. Zbl 1461.65241Liu, Hailiang; Huang, Yunqing; Lu, Wenying; Yi, Nianyu 4 2019 Mass- and energy-conserved numerical schemes for nonlinear Schrödinger equations. Zbl 1473.65102Feng, Xiaobing; Liu, Hailiang; Ma, Shu 4 2019 Computation of free surface waves around an arbitrary body by a Navier- Stokes solver using the pseudocompressibility technique. Zbl 0814.76066Liu, H.; Ikehata, M. 3 1994 Pattern formation, wave propagation and stability in conservation laws with slow diffusion and fast reaction. Zbl 1065.35156Fan, Haitao; Liu, Hailiang 3 2004 On a non-local selection-mutation model with a gradient flow structure. Zbl 1382.35313Jabin, Pierre-Emmanuel; Liu, Hailiang 3 2017 On traveling wave solutions of the \(\theta\)-equation of dispersive type. Zbl 1304.35190Ha, Tae Gab; Liu, Hailiang 3 2015 Efficient, positive, and energy stable schemes for multi-d Poisson-Nernst-Planck systems. Zbl 1471.35277Liu, Hailiang; Maimaitiyiming, Wumaier 5 2021 Unconditionally energy stable discontinuous Galerkin schemes for the Cahn-Hilliard equation. Zbl 1480.65264Liu, Hailiang; Yin, Peimeng 1 2021 Analysis of direct discontinuous Galerkin methods for multi-dimensional convection-diffusion equations. Zbl 1465.65100Liu, Hailiang 1 2021 Critical thresholds in one-dimensional damped Euler-Poisson systems. Zbl 1453.35145Bhatnagar, Manas; Liu, Hailiang 5 2020 Unconditional positivity-preserving and energy stable schemes for a reduced Poisson-Nernst-Planck system. Zbl 1473.65263Liu, Hailiang; Maimaitiyiming, Wumaier 3 2020 Unconditionally energy stable DG schemes for the Swift-Hohenberg equation. Zbl 1427.65372Liu, Hailiang; Yin, Peimeng 9 2019 A conservative discontinuous Galerkin method for nonlinear electromagnetic Schrödinger equations. Zbl 1435.35364Yi, Nianyu; Huang, Yunqing; Liu, Hailiang 4 2019 Third order maximum-principle-satisfying DG schemes for convection-diffusion problems with anisotropic diffusivity. Zbl 1452.65260Yu, Hui; Liu, Hailiang 4 2019 On accuracy of the mass-preserving DG method to multi-dimensional Schrödinger equations. Zbl 1461.65241Liu, Hailiang; Huang, Yunqing; Lu, Wenying; Yi, Nianyu 4 2019 Mass- and energy-conserved numerical schemes for nonlinear Schrödinger equations. Zbl 1473.65102Feng, Xiaobing; Liu, Hailiang; Ma, Shu 4 2019 A high order positivity preserving DG method for coagulation-fragmentation equations. Zbl 1426.65146Liu, Hailiang; Gröpler, Robin; Warnecke, Gerald 2 2019 An invariant-region-preserving limiter for DG schemes to isentropic Euler equations. Zbl 1416.76153Jiang, Yi; Liu, Hailiang 2 2019 Time-asymptotic convergence rates towards discrete steady states of a nonlocal selection-mutation model. Zbl 1427.35292Cai, Wenli; Jabin, Pierre-Emmanuel; Liu, Hailiang 2 2019 A mixed discontinuous Galerkin method without interior penalty for time-dependent fourth order problems. Zbl 1407.65168Liu, Hailiang; Yin, Peimeng 8 2018 Invariant-region-preserving DG methods for multi-dimensional hyperbolic conservation law systems, with an application to compressible Euler equations. Zbl 1416.65293Jiang, Yi; Liu, Hailiang 6 2018 Error estimates for the AEDG method to one-dimensional linear convection-diffusion equations. Zbl 1376.65122Liu, Hailiang; Wen, Hairui 3 2018 An invariant-region-preserving (IRP) limiter to DG methods for compressible Euler equations. Zbl 1407.65191Jiang, Yi; Liu, Hailiang 2 2018 Error estimates of the third order Runge-Kutta alternating evolution discontinuous Galerkin method for convection-diffusion problems. Zbl 1422.65261Liu, Hailiang; Wen, Hairui 1 2018 Error estimates for the iterative discontinuous Galerkin method to the nonlinear Poisson-Boltzmann equation. Zbl 07414376Yin, Peimeng; Huang, Yunqing; Liu, Hailiang 1 2018 Superconvergence of the direct discontinuous Galerkin method for convection-diffusion equations. Zbl 1361.65061Cao, Waixiang; Liu, Hailiang; Zhang, Zhimin 22 2017 A free energy satisfying discontinuous Galerkin method for one-dimensional Poisson-Nernst-Planck systems. Zbl 1406.82021Liu, Hailiang; Wang, Zhongming 20 2017 Tiling sets and spectral sets over finite fields. Zbl 1376.52038Aten, 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 1382.35313Jabin, Pierre-Emmanuel; Liu, Hailiang 3 2017 A finite volume method for nonlocal competition-mutation equations with a gradient flow structure. Zbl 1378.92047Cai, Wenli; Liu, Hailiang 2 2017 On the coupling of local multilevel mesh refinement and ZZ methods for unilateral frictional contact problems in elastostatics. Zbl 1439.74219Liu, H.; Ramière, I.; Lebon, F. 1 2017 Error estimates for Gaussian beam methods applied to symmetric strictly hyperbolic systems. Zbl 07213155Liu, Hailiang; Pryporov, Maksym 1 2017 A Hamiltonian preserving discontinuous Galerkin method for the generalized Korteweg-de Vries equation. Zbl 1349.65462Liu, Hailiang; Yi, Nianyu 15 2016 An entropy satisfying discontinuous Galerkin method for nonlinear Fokker-Planck equations. Zbl 1354.35158Liu, Hailiang; Wang, Zhongming 14 2016 An invariant preserving discontinuous Galerkin method for the Camassa-Holm equation. Zbl 1382.65321Liu, Hailiang; Xing, Yulong 9 2016 Alternating evolution discontinuous Galerkin methods for convection-diffusion equations. Zbl 1352.65356Liu, Hailiang; Pollack, Michael 5 2016 On invariant-preserving finite difference schemes for the Camassa-Holm equation and the two-component Camassa-Holm system. Zbl 1388.65059Liu, Hailiang; Pendleton, Terrance 5 2016 Global dynamics of Bose-Einstein condensation for a model of the Kompaneets equation. Zbl 1362.37161Levermore, C. David; Liu, Hailiang; Pego, Robert L. 4 2016 Sobolev and max norm error estimates for Gaussian beam superpositions. Zbl 1372.35263Liu, Hailiang; Runborg, Olof; Tanushev, Nicolay M. 2 2016 Oscillatory traveling wave solutions to an attractive chemotaxis system. Zbl 1350.35055Li, Tong; Liu, Hailiang; Wang, Lihe 1 2016 Optimal error estimates of the direct discontinuous Galerkin method for convection-diffusion equations. Zbl 1331.65141Liu, Hailiang 30 2015 Mass preserving discontinuous Galerkin methods for Schrödinger equations. Zbl 1352.65358Lu, Wenying; Huang, Yunqing; Liu, Hailiang 20 2015 A local discontinuous Galerkin method for the Burgers-Poisson equation. Zbl 1339.65177Liu, Hailiang; Ploymaklam, Nattapol 18 2015 The entropy satisfying discontinuous Galerkin method for Fokker-Planck equations. Zbl 1320.65143Liu, Hailiang; Yu, Hui 17 2015 Thresholds for shock formation in traffic flow models with Arrhenius look-ahead dynamics. Zbl 1304.35420Lee, Yongki; Liu, Hailiang 11 2015 Time-asymptotic convergence rates towards the discrete evolutionary stable distribution. Zbl 1328.65268Cai, Wenli; Jabin, Pierre-Emmanuel; Liu, Hailiang 4 2015 Threshold for shock formation in the hyperbolic Keller-Segel model. Zbl 1330.35250Lee, Yongki; Liu, Hailiang 4 2015 On traveling wave solutions of the \(\theta\)-equation of dispersive type. Zbl 1304.35190Ha, Tae Gab; Liu, Hailiang 3 2015 Entropy satisfying schemes for computing selection dynamics in competitive interactions. Zbl 1318.65085Liu, Hailiang; Cai, Wenli; Su, Ning 3 2015 Error estimates of the Bloch band-based Gaussian beam superposition for the Schrödinger equation. Zbl 1348.35213Liu, Hailiang; Pryporov, Maksym 2 2015 A free energy satisfying finite difference method for Poisson-Nernst-Planck equations. Zbl 1349.65317Liu, Hailiang; Wang, Zhongming 33 2014 Maximum-principle-satisfying third order discontinuous Galerkin schemes for Fokker-Planck equations. Zbl 1341.65038Liu, Hailiang; Yu, Hui 18 2014 Alternating evolution discontinuous Galerkin methods for Hamilton-Jacobi equations. Zbl 1349.65461Liu, Hailiang; Pollack, Michael 7 2014 An iterative discontinuous Galerkin method for solving the nonlinear Poisson Boltzmann equation. Zbl 1388.65162Yin, Peimeng; Huang, Yunqing; Liu, Hailiang 6 2014 A conservative discontinuous Galerkin method for the Degasperis-Procesi equation. Zbl 1296.35158Huang, Yunqing; Liu, Hailiang; Yi, Nianyu 4 2014 Gaussian beam methods for the Helmholtz equation. Zbl 1302.35135Liu, Hailiang; Ralston, James; Runborg, Olof; Tanushev, Nicolay M. 4 2014 Entropy/energy stable schemes for evolutionary dispersal models. Zbl 1349.65318Liu, Hailiang; Yu, Hui 1 2014 Numerical simulations of traveling wave solutions in a drift paradox inspired diffusive delay population model. Zbl 07312544Jackiewicz, Z.; Liu, H.; Li, B.; Kuang, Y. 1 2014 A direct discontinuous Galerkin method for the generalized Korteweg-de Vries equation: energy conservation and boundary effect. Zbl 1297.65122Yi, Nianyu; Huang, Yunqing; Liu, Hailiang 25 2013 Error estimates for Gaussian beam superpositions. Zbl 1277.35236Liu, Hailiang; Runborg, Olof; Tanushev, Nicolay M. 21 2013 Thresholds in three-dimensional restricted Euler-Poisson equations. Zbl 1434.35105Lee, Yongki; Liu, Hailiang 4 2013 A uniform multiscale method for 2D static and dynamic analyses of heterogeneous materials. Zbl 1352.74459Zhang, H. W.; Liu, H.; Wu, J. K. 3 2013 Alternating evolution schemes for Hamilton-Jacobi equations. Zbl 1270.65049Liu, Hailiang; Pollack, Michael; Saran, Haseena 2 2013 Recovery of normal derivatives from the piecewise \(L^2\) projection. Zbl 1408.65009Huang, Yunqing; Liu, Hailiang; Yi, Nianyu 12 2012 An entropy satisfying conservative method for the Fokker-Planck equation of the finitely extensible nonlinear elastic dumbbell model. Zbl 1422.74097Liu, Hailiang; Yu, Hui 9 2012 Numerical approximation of the Euler-Poisson-Boltzmann model in the quasineutral limit. Zbl 1395.76047Degond, P.; Liu, H.; Savelief, D.; Vignal, M.-H. 8 2012 Global well-posedness for the microscopic FENE model with a sharp boundary condition. Zbl 1233.35109Liu, Hailiang; Shin, Jaemin 6 2012 The Cauchy-Dirichlet problem for the finitely extensible nonlinear elastic dumbbell model of polymeric fluids. Zbl 1257.35144Liu, Hailiang; Shin, Jaemin 2 2012 Alternating evolution schemes for hyperbolic conservation laws. Zbl 1248.65092Saran, Haseena; Liu, Hailiang 5 2011 A level set approach for dilute non-collisional fluid-particle flows. Zbl 1391.76348Liu, Hailiang; Wang, Zhongming; Fox, Rodney O. 1 2011 The direct discontinuous Galerkin (DDG) method for diffusion with interface corrections. Zbl 1364.65200Liu, Hailiang; Yan, Jue 68 2010 Recovery of high frequency wave fields from phase space-based measurements. Zbl 1221.35031Liu, Hailiang; Ralston, James 12 2010 Recovery of high frequency wave fields for the acoustic wave equation. Zbl 1213.35284Liu, Hailiang; Ralston, James 8 2010 Global regularity of the 4D restricted Euler equations. Zbl 1193.37123Liu, Hailiang; Tadmor, Eitan; Wei, Dongming 7 2010 Global regularity, and wave breaking phenomena in a class of nonlocal dispersive equations. Zbl 1218.35175Liu, Hailiang; Yin, Zhaoyang 6 2010 The direct discontinuous Galerkin (DDG) methods for diffusion problems. Zbl 1189.65227Liu, Hailiang; Yan, Jue 85 2009 Kinetic models for polymers with inertial effects. Zbl 1183.76614Degond, Pierre; Liu, Hailiang 12 2009 Critical thresholds in hyperbolic relaxation systems. Zbl 1170.35062Li, Tong; Liu, Hailiang 9 2009 Critical thresholds in a relaxation system with resonance of characteristic speeds. Zbl 1171.35428Li, Tong; Liu, Hailiang 4 2009 Development of an analytical \(\beta\)-function PDF integration algorithm for simulation of non-premixed turbulent combustion. Zbl 1405.80011Lien, 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 1271.76285Shyy, W.; Lian, Y.; Tang, J.; Liu, H.; Trizila, P.; Stanford, B.; Bernal, L.; Cesnik, C.; Friedmann, P.; Ifju, P. 15 2008 On discreteness of the Hopf equation. Zbl 1149.65071Liu, Hai-liang 10 2008 Robust control of robotic manipulators based on integral sliding mode. Zbl 1154.93344Shi, J.; Liu, H.; Bajcinca, N. 6 2008 Critical thresholds in a relaxation model for traffic flows. Zbl 1152.35006Li, Tong; Liu, Hailiang 5 2008 A nonlocal conservation law with nonlinear “radiation” inhomogeneity. Zbl 1158.35063di Francesco, Marco; Fellner, Klemens; Liu, Hailiang 5 2008 Boundary conditions for the microscopic FENE models. Zbl 1147.76003Liu, Chun; Liu, Hailiang 5 2008 Superposition of multi-valued solutions in high frequency wave dynamics. Zbl 1203.65141Liu, Hailiang; Wang, Zhongming 5 2008 Global attractor for a nonlinear thermoviscoelastic system in shape memory alloys. Zbl 1173.35386Qin, Yuming; Liu, Hailiang; Song, Changming 4 2008 An alternating evolution approximation to systems of hyperbolic conservation laws. Zbl 1162.35049Liu, Hailiang 3 2008 Rigorous derivation of the hydrodynamical equations for rotating superfluids. Zbl 1144.81462Liu, Hailiang; Sparber, Christof 2 2008 A Bloch band based level set method for computing the semiclassical limit of Schrödinger equations. Zbl 1168.65056Liu, Hailiang; Wang, Zhongming 1 2008 Computing multi-valued velocity and electric fields for 1D Euler-Poisson equations. Zbl 1146.78012Liu, Hailiang; Wang, Zhongming 5 2007 A field-space-based level set method for computing multi-valued solutions to 1D Euler-Poisson equations. Zbl 1140.81399Liu, Hailiang; Wang, Zhongming 5 2007 Global orientation dynamics for liquid crystalline polymers. Zbl 1183.82101Liu, Hailiang 4 2007 The modular multisensory DLR-HIT-Hand. Zbl 1183.70026Liu, 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 1092.65083Liu, Hailiang; Yan, Jue 26 2006 Wave breaking in a class of nonlocal dispersive wave equations. Zbl 1110.35069Liu, Hailiang 23 2006 Multi-valued solution and level set methods in computational high frequency wave propagation. Zbl 1120.65110Liu, H.; Osher, S.; Tsai, R. 13 2006 A level set framework for capturing multi-valued solutions of nonlinear first-order equations. Zbl 1109.65080Liu, Hailiang; Cheng, Li-Tien; Osher, Stanley 7 2006 Critical thresholds in the semiclassical limit of 2D rotational Schrödinger equations. Zbl 1089.35052Liu, Hailiang 4 2006 Sharp interface Cartesian grid method. I: An easily implemented technique for 3D moving boundary computations. Zbl 1154.76359Marella, S.; Krishnan, S.; Liu, H.; Udaykumar, H. S. 72 2005 Sharp interface Cartesian grid method. II: A technique for simulating droplet interactions with surfaces of arbitrary shape. Zbl 1154.76358Liu, H.; Krishnan, S.; Marella, S.; Udaykumar, H. S. 35 2005 Computing multivalued physical observables for the semiclassical limit of the Schrödinger equation. Zbl 1072.65132Jin, Shi; Liu, Hailiang; Osher, Stanley; Tsai, Yen-Hsi Richard 35 2005 Axial symmetry and classification of stationary solutions of Doi-Onsager equation on the sphere with Maier-Saupe potential. Zbl 1092.76007Liu, Hailiang; Zhang, Hui; Zhang, Pingwen 26 2005 Computing multi-valued physical observables for the high frequency limit of symmetric hyperbolic systems. Zbl 1098.65094Jin, Shi; Liu, Hailiang; Osher, Stanley; Tsai, Richard 20 2005 Stability of a traffic flow model with nonconvex relaxation. Zbl 1099.35156Li, Tong; Liu, Hailiang 7 2005 ...and 48 more Documents all cited Publications top 5 cited Publications all top 5 Cited by 990 Authors 76 Liu, Hailiang 21 Shen, Chun 20 Yang, Hanchun 18 Sun, Meina 17 Shu, Chi-Wang 16 Zhang, Yu 15 Huang, Yunqing 14 Yi, Nianyu 12 Cheng, Hongjun 12 Jin, Shi 12 Yin, Gan 11 Liu, Tiegang 11 Wang, Jinhuan 11 Wang, Zhongming 11 Yan, Jue 10 Zhang, Yanyan 9 Cheng, Jian 9 Guo, Lihui 9 Shao, Zhiqiang 9 Yu, Xijun 9 Zhang, Pingwen 8 Huang, Chaobao 8 Li, Tong 8 Pang, Yicheng 8 Tadmor, Eitan 8 Xu, Yan 7 An, Na 7 Cheng, Yingda 7 Choi, Young-Pil 7 Lee, Yongki 7 Meng, Xiong 7 Nedeljkov, Marko 7 Runborg, Olof 7 Yin, Peimeng 6 Carrillo de la Plata, José Antonio 6 Degond, Pierre 6 Fox, Rodney O. 6 Osher, Stanley Joel 6 Sarrico, Carlos Orlando R. 6 Sheng, Wancheng 6 Tan, Changhui 6 Wang, Wei 6 Wu, Boying 6 Yang, Xu 5 Cheng, Yao 5 Liu, Jinjing 5 Luo, Hong 5 Mitrovic, Darko 5 Qian, Jianliang 5 Rozanova, Olga S. 5 Süli, Endre E. 5 Titi, Edriss Saleh 5 Wen, Xin 5 Xia, Yinhua 5 Xing, Yulong 5 Zhang, Mengping 5 Zhang, Qian 5 Zhang, Rongpei 5 Zhang, Zhiyue 5 Zhou, Shenggao 5 Zhou, Zhennan 5 Zhu, Changjiang 4 Baccouch, Mahboub 4 Barrett, John W. 4 Bhatnagar, Manas 4 Dai, Limei 4 Du, Qiang 4 Gosse, Laurent 4 He, Dongdong 4 Kim, Junseok 4 Kwon, Bongsuk 4 Motamed, Mohammad 4 Nishikawa, Hiroaki 4 Pan, Kejia 4 Pu, Xueke 4 Ruan, Lizhi 4 Shu, Shi 4 Tao, Qi 4 Tsai, Yen-Hsi Richard 4 Xu, Jie 4 Yan, Jinliang 4 Yang, Ying 4 Yong, Wen-An 4 Yu, Hui 4 Yue, Huiqiang 4 Yuen, Manwai 4 Zhang, Dazhi 4 Zhang, Fan 4 Zhang, Qiang 4 Zhang, Zhifei 4 Zhou, Hong 4 Zhu, Jiang 3 Barbieri, Luca 3 Cao, Waixiang 3 Chen, Zheng 3 Cheng, Bin 3 Cockburn, Bernardo 3 Dehghan Takht Fooladi, Mehdi 3 Feng, Xiaobing 3 Gottlieb, Sigal ...and 890 more Authors all top 5 Cited in 151 Serials 86 Journal of Computational Physics 52 Journal of Scientific Computing 50 Journal of Differential Equations 34 Journal of Mathematical Analysis and Applications 23 Journal of Mathematical Physics 21 M\(^3\)AS. 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Fluids 4 Journal of Applied Analysis and Computation 3 Nonlinearity 3 Advances in Mathematics 3 Numerical Methods for Partial Differential Equations 3 Communications in Partial Differential Equations 3 International Journal of Computer Mathematics 3 Advances in Computational Mathematics 3 Mathematical Problems in Engineering 3 Mathematics and Mechanics of Solids 3 Journal of Mathematical Fluid Mechanics 3 Communications in Nonlinear Science and Numerical Simulation 3 Journal of Nonlinear Mathematical Physics 3 Multiscale Modeling & Simulation 3 Kinetic and Related Models 3 Open Mathematics 2 Journal of Statistical Physics 2 Bulletin of Mathematical Biology 2 Mathematics and Computers in Simulation 2 Annales de l’Institut Henri Poincaré. Analyse Non Linéaire 2 International Journal of Mathematics 2 Computational Mathematics and Mathematical Physics 2 Proceedings of the Royal Society of Edinburgh. Section A. Mathematics 2 Journal of Dynamics and Differential Equations 2 Applied and Computational Harmonic Analysis 2 ZAMM. Zeitschrift für Angewandte Mathematik und Mechanik 2 International Journal of Nonlinear Sciences and Numerical Simulation 2 Discrete and Continuous Dynamical Systems. Series B 2 Comptes Rendus. Mathématique. Académie des Sciences, Paris 2 Thai Journal of Mathematics 2 Acta Numerica 2 Discrete and Continuous Dynamical Systems. Series S 2 Research in the Mathematical Sciences 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 Physica A 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 Calcolo 1 Duke Mathematical Journal 1 International Journal for Numerical Methods in Engineering 1 Inventiones Mathematicae 1 Journal of Functional Analysis ...and 51 more Serials all top 5 Cited in 33 Fields 606 Partial differential equations (35-XX) 359 Numerical analysis (65-XX) 287 Fluid mechanics (76-XX) 83 Statistical mechanics, structure of matter (82-XX) 43 Biology and other natural sciences (92-XX) 30 Optics, electromagnetic theory (78-XX) 22 Mechanics of deformable solids (74-XX) 22 Quantum theory (81-XX) 21 Dynamical systems and ergodic theory (37-XX) 16 Operations research, mathematical programming (90-XX) 14 Ordinary differential equations (34-XX) 14 Functional analysis (46-XX) 11 Geophysics (86-XX) 10 Relativity and gravitational theory (83-XX) 9 Calculus of variations and optimal control; optimization (49-XX) 8 Astronomy and astrophysics (85-XX) 7 Probability theory and stochastic processes (60-XX) 6 Approximations and expansions (41-XX) 6 Integral equations (45-XX) 5 Global analysis, analysis on manifolds (58-XX) 4 Real functions (26-XX) 4 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 3 Mechanics of particles and systems (70-XX) 3 Systems theory; control (93-XX) 2 Harmonic analysis on Euclidean spaces (42-XX) 2 Operator theory (47-XX) 2 Computer science (68-XX) 2 Classical thermodynamics, heat transfer (80-XX) 1 Mathematical logic and foundations (03-XX) 1 Linear and multilinear algebra; matrix theory (15-XX) 1 Topological groups, Lie groups (22-XX) 1 Measure and integration (28-XX) 1 Difference and functional equations (39-XX) Citations by Year