Edit Profile (opens in new tab) Lowengrub, John Samuel Compute Distance To: Compute Author ID: lowengrub.john-s Published as: Lowengrub, John; Lowengrub, John S.; Lowengrub, J. S.; Lowengrub, J. more...less Homepage: http://www.math.uci.edu/~lowengrb/ External Links: MGP Documents Indexed: 111 Publications since 1989 Co-Authors: 107 Co-Authors with 110 Joint Publications 3,317 Co-Co-Authors all top 5 Co-Authors 1 single-authored 18 Wise, Steven M. 15 Li, Shuwang 14 Hou, Thomas Yizhao 12 Cristini, Vittorio 12 Voigt, Axel 9 Wang, Cheng 8 Shelley, Michael J. 7 Macklin, Paul 6 Guo, Zhenlin 5 Beale, J. Thomas 5 Guan, Zhen 5 Li, Xiaofan 4 Aland, Sebastian 4 Chen, Ying 4 Frieboes, Hermann B. 4 Goodman, Jonathan B. 4 Kim, Junseok 4 Li, Xiangrong 4 Lin, Ping 4 Zhao, Meng 4 Zheng, Xiaoming 3 Baskaran, Arvind 3 Belmonte, Andrew 3 Chaplain, Mark A. J. 3 Hu, Zhengzheng 3 James, Ashley J. 3 Jin, Fang 3 Konstorum, Anna 3 Leo, Perry H. 3 Liu, Chun 3 Nie, Qing 3 Rätz, Andreas 3 Xu, Jianjun 3 Zhao, Hongkai 2 Allard, Jun 2 Caflisch, Russel E. 2 Chuang, Yao-Li 2 Feng, Wenqiang 2 Kang, Kyungkeun 2 Lee, Hyeong-Gi 2 Li, Zhilin 2 Lu, Min-Jhe 2 McDougall, Steven R. 2 Pham, Kara 2 Sohn, Jinsun 2 Teigen, Knut Erik 2 Truskinovsky, Lev 2 Turian, Emma 2 Ying, Wenjun 2 Zhao, Kun 1 Anderson, Alexander R. A. 1 Anderson, Anthony M. 1 Angenent, Sigurd Bernardus 1 Aronson, Donald G. 1 Barua, Amlan K. 1 Bellomo, Nicola 1 Betelú, Santiago I. 1 Bingham, Richard 1 Byrne, Helen Mary 1 Chauvière, Arnaud 1 Cheng, Qing 1 Cox, Geoffrey 1 Dosi, Giovanni 1 Egerer, Sabine 1 Feng, Hualong 1 Forni, Guido 1 Franco-de-Leon, Mariano 1 Hao, Wenrui 1 Hatzikirou, Haralambos 1 Hausser, Frank 1 He, Ong 1 Heinonen, Vili 1 Hillen, Thomas 1 Jackson, Trachette L. 1 Jou, Herng-Jeng 1 Knopoff, Damian A. 1 Komarova, Natalia L. 1 Krasny, Robert 1 Lander, Arthur D. 1 Lervåg, Karl Yngve 1 Leung, Shingyu 1 Li, Bo 1 Li, Jonathan F. 1 Longmire, Ellen K. 1 Lopes Filho, Milton da Costa 1 Marth, Wieland 1 Merriman, Barry 1 Niroobakhsh, Zahra 1 Nussenzveig Lopes, Helena Judith 1 Shelly, M. J. 1 Shen, Jie 1 Song, Peng 1 Titi, Edriss Saleh 1 Torabi, Solmaz 1 Tseng, Yu-Hau 1 Twarock, Reidun 1 van den Driessche, Pauline 1 Virgillito, Maria Enrica 1 Wang, Fan 1 Weiss, Lora D. ...and 7 more Co-Authors all top 5 Serials 29 Journal of Computational Physics 11 Journal of Theoretical Biology 5 Journal of Mathematical Biology 5 SIAM Journal on Numerical Analysis 5 Communications in Mathematical Sciences 4 Physics of Fluids 4 Communications in Computational Physics 3 Communications on Pure and Applied Mathematics 3 Bulletin of Mathematical Biology 3 SIAM Journal on Scientific Computing 2 Computer Methods in Applied Mechanics and Engineering 2 Journal of Fluid Mechanics 2 Nonlinearity 2 Journal of Computational and Applied Mathematics 2 Physica D 2 Mathematical and Computer Modelling 2 Journal of Scientific Computing 2 Advances in Computational Mathematics 2 Proceedings of the Royal Society of London. Series A. Mathematical, Physical and Engineering Sciences 1 Mathematical Methods in the Applied Sciences 1 Mathematics of Computation 1 European Journal of Applied Mathematics 1 M\(^3\)AS. Mathematical Models & Methods in Applied Sciences 1 SIAM Journal on Applied Mathematics 1 Interfaces and Free Boundaries 1 CMES. Computer Modeling in Engineering & Sciences 1 Discrete and Continuous Dynamical Systems. Series B 1 European Series in Applied and Industrial Mathematics (ESAIM): Mathematical Modelling and Numerical Analysis 1 FDMP. Fluid Dynamics & Materials Processing 1 Journal of Biological Dynamics 1 Statistical Analysis and Data Mining 1 International Journal for Numerical Methods in Biomedical Engineering 1 International Journal of Biomathematics and Biostatistics all top 5 Fields 58 Fluid mechanics (76-XX) 49 Numerical analysis (65-XX) 40 Biology and other natural sciences (92-XX) 37 Partial differential equations (35-XX) 13 Mechanics of deformable solids (74-XX) 9 Statistical mechanics, structure of matter (82-XX) 4 Classical thermodynamics, heat transfer (80-XX) 3 Integral equations (45-XX) 2 Systems theory; control (93-XX) 1 Ordinary differential equations (34-XX) 1 Dynamical systems and ergodic theory (37-XX) 1 Statistics (62-XX) 1 Computer science (68-XX) 1 Quantum theory (81-XX) Publications by Year all cited Publications top 5 cited Publications Citations contained in zbMATH Open 100 Publications have been cited 3,875 times in 2,042 Documents Cited by ▼ Year ▼ Quasi-incompressible Cahn-Hilliard fluids and topological transitions. Zbl 0927.76007Lowengrub, J.; Truskinovsky, L. 325 1998 An energy-stable and convergent finite-difference scheme for the phase field crystal equation. Zbl 1201.35027Wise, S. M.; Wang, Cheng; Lowengrub, J. S. 223 2009 Removing the stiffness from interfacial flows with surface tension. Zbl 0810.76095Hou, Thomas Y.; Lowengrub, John S.; Shelley, Michael J. 205 1994 Stable and efficient finite-difference nonlinear-multigrid schemes for the phase field crystal equation. Zbl 1171.82015Hu, Z.; Wise, S. M.; Wang, C.; Lowengrub, J. S. 171 2009 Three-dimensional multispecies nonlinear tumor growth. I: Model and numerical method. Zbl 1398.92135Wise, S. M.; Lowengrub, J. S.; Frieboes, H. B.; Cristini, Vittorio 154 2008 Nonlinear modelling of cancer: bridging the gap between cells and tumours. Zbl 1181.92046Lowengrub, J. S.; Frieboes, H. B.; Jin, F.; Chuang, Y-L; Li, X.; Macklin, P.; Wise, S. M.; Cristini, V. 140 2010 Conservative multigrid methods for Cahn–Hilliard fluids. Zbl 1109.76348Kim, Junseok; Kang, Kyungkeun; Lowengrub, John 134 2004 Nonlinear simulations of solid tumor growth using a mixture model: invasion and branching. Zbl 1311.92039Cristini, Vittorio; Li, Xiangrong; Lowengrub, John S.; Wise, Steven M. 107 2009 Nonlinear simulation of tumor growth. Zbl 1023.92013Cristini, Vittorio; Lowengrub, John; Nie, Qing 97 2003 Convergence analysis of a second order convex splitting scheme for the modified phase field crystal equation. Zbl 1401.82046Baskaran, A.; Lowengrub, J. S.; Wang, C.; Wise, S. M. 96 2013 Solving the regularized, strongly anisotropic Cahn-Hilliard equation by an adaptive nonlinear multigrid method. Zbl 1310.82044Wise, Steven; Kim, Junseok; Lowengrub, John 84 2007 Second order convex splitting schemes for periodic nonlocal Cahn-Hilliard and Allen-Cahn equations. Zbl 1349.65298Guan, Zhen; Lowengrub, John S.; Wang, Cheng; Wise, Steven M. 83 2014 A level-set method for interfacial flows with surfactant. Zbl 1161.76548Xu, Jian-Jun; Li, Zhilin; Lowengrub, John; Zhao, Hongkai 81 2006 A surfactant-conserving volume-of-fluid method for interfacial flows with insoluble surfactant. Zbl 1061.76062James, Ashley J.; Lowengrub, John 79 2004 A diffuse-interface method for two-phase flows with soluble surfactants. Zbl 1428.76210Teigen, Knut Erik; Song, Peng; Lowengrub, John; Voigt, Axel 75 2011 Multiscale modelling and nonlinear simulation of vascular tumour growth. Zbl 1311.92040Macklin, Paul; McDougall, Steven; Anderson, Alexander R. A.; Chaplain, Mark A. J.; Cristini, Vittorio; Lowengrub, John 73 2009 Energy stable and efficient finite-difference nonlinear multigrid schemes for the modified phase field crystal equation. Zbl 1349.65265Baskaran, Arvind; Hu, Zhengzheng; Lowengrub, John S.; Wang, Cheng; Wise, Steven M.; Zhou, Peng 72 2013 Phase field modeling and simulation of three-phase flows. Zbl 1100.35088Kim, Junseok; Lowengrub, John 68 2005 Solving PDEs in complex geometries: a diffuse domain approach. Zbl 1178.35027Li, X.; Lowengrub, J.; Rätz, A.; Voigt, A. 67 2009 The long-time motion of vortex sheets with surface tension. Zbl 1185.76545Hou, T. Y.; Lowengrub, J. S.; Shelly, M. J. 67 1997 Boundary integral methods for multicomponent fluids and multiphase materials. Zbl 1046.76029Hou, T. Y.; Lowengrub, J. S.; Shelley, M. J. 66 2001 Growth rates for the linearized motion of fluid interfaces away from equilibrium. Zbl 0796.76041Beale, J. Thomas; Hou, Thomas Y.; Lowengrub, John S. 62 1993 Modeling pinchoff and reconnection in a Hele-Shaw cell. I: The models and their calibration. Zbl 1184.76316Lee, Hyeong-Gi; Lowengrub, J. S.; Goodman, J. 61 2002 A new phase-field model for strongly anisotropic systems. Zbl 1186.80014Torabi, Solmaz; Lowengrub, John; Voigt, Axel; Wise, Steven 61 2009 Modeling pinchoff and reconnection in a Hele-Shaw cell. II: Analysis and simulation in the nonlinear regime. Zbl 1184.76317Lee, Hyeong-Gi; Lowengrub, J. S.; Goodman, J. 53 2002 An adaptive coupled level-set/volume-of-fluid interface capturing method for unstructured triangular grids. Zbl 1160.76377Yang, Xiaofeng; James, Ashley J.; Lowengrub, John; Zheng, Xiaoming; Cristini, Vittorio 51 2006 Convergence of the point vortex method for the 2-D Euler equations. Zbl 0694.76013Goodman, Jonathan; Hou, Thomas Y.; Lowengrub, John 47 1990 An adaptive multigrid algorithm for simulating solid tumor growth using mixture models. Zbl 1211.65123Wise, S. M.; Lowengrub, J. S.; Cristini, V. 45 2011 A diffuse-interface approach for modelling transport, diffusion and adsorption/desorption of material quantities on a deformable interface. Zbl 1186.35168Teigen, Knut Erik; Li, Xiangrong; Lowengrub, John; Wang, Fan; Voigt, Axel 44 2009 Microstructural evolution in inhomogeneous elastic media. Zbl 0880.73050Jou, H.-J.; Leo, P. H.; Lowengrub, J. S. 43 1997 Three-dimensional multispecies nonlinear tumor growth. II: Tumor invasion and angiogenesis. Zbl 1406.92049Frieboes, Hermann B.; Jin, Fang; Chuang, Yao-Li; Wise, Steven M.; Lowengrub, John S.; Cristini, Vittorio 43 2010 A numerical method for the quasi-incompressible Cahn-Hilliard-Navier-Stokes equations for variable density flows with a discrete energy law. Zbl 1349.76057Guo, Z.; Lin, P.; Lowengrub, J. S. 41 2014 Analysis of a mixture model of tumor growth. Zbl 1292.35153Lowengrub, John; Titi, Edriss; Zhao, Kun 40 2013 Evolving interfaces via gradients of geometry-dependent interior Poisson problems: application to tumor growth. Zbl 1067.65111Macklin, Paul; Lowengrub, John 38 2005 Conservative multigrid methods for ternary Cahn-Hilliard systems. Zbl 1085.65093Kim, Junseok; Kang, Kyungkeun; Lowengrub, John 37 2004 A multiscale model of virus pandemic: heterogeneous interactive entities in a globally connected world. Zbl 1451.92276Bellomo, Nicola; Bingham, Richard; Chaplain, Mark A. J.; Dosi, Giovanni; Forni, Guido; Knopoff, Damian A.; Lowengrub, John; Twarock, Reidun; Virgillito, Maria Enrica 37 2020 Adaptive unstructured volume remeshing. II: Application to two- and three-dimensional level-set simulations of multiphase flow. Zbl 1075.65120Zheng, Xiaoming; Lowengrub, John; Anderson, Anthony; Cristini, Vittorio 36 2005 A grid based particle method for solving partial differential equations on evolving surfaces and modeling high order geometrical motion. Zbl 1316.65089Leung, Shingyu; Lowengrub, John; Zhao, Hongkai 36 2011 Convergence of a boundary integral method for water waves. Zbl 0858.76046Beale, J. Thomas; Hou, Thomas Y.; Lowengrub, John 32 1996 Diffuse interface models of locally inextensible vesicles in a viscous fluid. Zbl 1349.76933Aland, Sebastian; Egerer, Sabine; Lowengrub, John; Voigt, Axel 32 2014 An improved geometry-aware curvature discretization for level set methods: Application to tumor growth. Zbl 1089.92024Macklin, Paul; Lowengrub, John 31 2006 Convergence analysis for second-order accurate schemes for the periodic nonlocal Allen-Cahn and Cahn-Hilliard equations. Zbl 1387.65087Guan, Zhen; Lowengrub, John; Wang, Cheng 31 2017 Mass conservative and energy stable finite difference methods for the quasi-incompressible Navier-Stokes-Cahn-Hilliard system: primitive variable and projection-type schemes. Zbl 1439.76121Guo, Z.; Lin, P.; Lowengrub, J.; Wise, S. M. 25 2017 A new ghost cell/level set method for moving boundary problems: application to tumor growth. Zbl 1203.65144Macklin, Paul; Lowengrub, John S. 25 2008 A uniquely solvable, energy stable numerical scheme for the functionalized Cahn-Hilliard equation and its convergence analysis. Zbl 1398.65208Feng, Wenqiang; Guan, Zhen; Lowengrub, John; Wang, Cheng; Wise, Steven M.; Chen, Ying 24 2018 Two-phase flow in complex geometries: a diffuse domain approach. Zbl 1231.76200Aland, S.; Lowengrub, J.; Voigt, A. 24 2010 Dynamics of multicomponent vesicles in a viscous fluid. Zbl 1381.76053Sohn, Jin Sun; Tseng, Yu-Hau; Li, Shuwang; Voigt, Axel; Lowengrub, John S. 22 2010 Numerical evidence of nonuniqueness in the evolution of vortex sheets. Zbl 1124.76010Lopes Filho, Milton C.; Lowengrub, John; Nussenzveig Lopes, Helena J.; Zheng, Yuxi 22 2006 Efficient energy stable schemes for isotropic and strongly anisotropic Cahn-Hilliard systems with the Willmore regularization. Zbl 1395.65014Chen, Ying; Lowengrub, John; Shen, Jie; Wang, Cheng; Wise, Steven 20 2018 Microstructural evolution in orthotropic elastic media. Zbl 0960.74076Leo, P. H.; Lowengrub, J. S.; Nie, Qing 19 2000 Nonlinear three-dimensional simulation of solid tumor growth. Zbl 1124.92022Li, Xiangrong; Cristini, Vittorio; Nie, Qing; Lowengrub, John S. 19 2007 A rescaling scheme with application to the long-time simulation of viscous fingering in a Hele-Shaw cell. Zbl 1343.76048Li, Shuwang; Lowengrub, John S.; Leo, Perry H. 18 2007 A mass-conservative adaptive FAS multigrid solver for cell-centered finite difference methods on block-structured, locally-Cartesian grids. Zbl 1380.65402Feng, Wenqiang; Guo, Zhenlin; Lowengrub, John S.; Wise, Steven M. 17 2018 Convergence of the vortex method for vortex sheets. Zbl 0676.76023Caflisch, Russel E.; Lowengrub, John S. 15 1989 Geometric evolution laws for thin crystalline films: modeling and numerics. Zbl 1364.74062Li, Bo; Lowengrub, John; Ratz, Andreas; Voigt, Axel 15 2009 Multispecies model of cell lineages and feedback control in solid tumors. Zbl 1397.92381Youssefpour, H.; Li, X.; Lander, A. D.; Lowengrub, J. S. 14 2012 Convergence of the point vortex method for the 3-D Euler equations. Zbl 0856.76059Hou, Thomas Y.; Lowengrub, John 12 1990 High-order and efficient methods for the vorticity formulation of the Euler equations. Zbl 0815.76068Lowengrub, J. S.; Shelley, M. J.; Merriman, B. 11 1993 Analysis of the diffuse-domain method for solving PDEs in complex geometries. Zbl 1328.65223Lervåg, Karl Yngve; Lowengrub, John 11 2015 Focusing of an elongated hole in porous medium flow. Zbl 0989.35082Angenent, S. B.; Aronson, D. G.; Betelu, S. I.; Lowengrub, J. S. 10 2001 A continuum model of colloid-stabilized interfaces. Zbl 1308.76159Aland, Sebastian; Lowengrub, John; Voigt, Axel 10 2011 The effect of interstitial pressure on tumor growth: coupling with the blood and lymphatic vascular systems. Zbl 1406.92330Wu, Min; Frieboes, Hermann B.; McDougall, Steven R.; Chaplain, Mark A. J.; Cristini, Vittorio; Lowengrub, John 10 2013 Convergence of a point vortex method for vortex sheets. Zbl 0799.76062Hou, Thomas Y.; Lowengrub, John; Krasny, Robert 9 1991 Feedback regulation in a cancer stem cell model can cause an Allee effect. Zbl 1341.92029Konstorum, Anna; Hillen, Thomas; Lowengrub, John 9 2016 Surface phase separation and flow in a simple model of multicomponent drops and vesicles. Zbl 1153.76441Lowengrub, J. S.; Xu, J-J.; Voigt, A. 9 2007 Numerical study of surfactant-laden drop-drop interactions. Zbl 1364.76165Xu, Jian-Jun; Li, Zhilin; Lowengrub, John; Zhao, Hongkai 8 2011 Numerical simulation of endocytosis: viscous flow driven by membranes with non-uniformly distributed curvature-inducing molecules. Zbl 1351.76067Lowengrub, John; Allard, Jun; Aland, Sebastian 8 2016 Spatial and temporal stability issues for interfacial flows with surface tension. Zbl 0816.76050Beale, J. T.; Hou, T. Y.; Lowengrub, J. S.; Shelley, M. J. 7 1994 Computation of a shrinking interface in a Hele-Shaw cell. Zbl 1396.76029Zhao, Meng; Li, Xiaofan; Ying, Wenjun; Belmonte, Andrew; Lowengrub, John; Li, Shuwang 7 2018 Topological transitions in liquid/liquid interfaces. Zbl 0929.35191Lowengrub, J. S.; Goodman, J.; Lee, H.; Longmire, E. K.; Shelley, M. J.; Truskinovsky, L. 7 1999 Tumor growth in complex, evolving microenvironmental geometries: a diffuse domain approach. Zbl 1303.92042Chen, Ying; Lowengrub, John S. 7 2014 An interface-fitted adaptive mesh method for elliptic problems and its application in free interface problems with surface tension. Zbl 1357.65271Zheng, Xiaoming; Lowengrub, John 7 2016 An energy stable, hexagonal finite difference scheme for the 2D phase field crystal amplitude equations. Zbl 1349.74360Guan, Zhen; Heinonen, Vili; Lowengrub, John; Wang, Cheng; Wise, Steven M. 7 2016 Density-dependent quiescence in glioma invasion: instability in a simple reaction-diffusion model for the migration/proliferation dichotomy. Zbl 1448.92064Pham, Kara; Chauviere, Arnaud; Hatzikirou, Haralambos; Li, Xiangrong; Byrne, Helen M.; Cristini, Vittorio; Lowengrub, John 6 2012 Modeling an elastic fingering instability in a reactive Hele-Shaw flow. Zbl 1343.76011He, Ong; Lowengrub, John; Belmonte, Andrew 6 2012 Thermodynamically consistent models for two-component vesicles. Zbl 1306.92014Haußer, Frank; Marth, Wieland; Li, Shuwang; Lowengrub, John; Rätz, Andreas; Voigt, Axel 5 2013 Nonlinear simulations of elastic fingering in a Hele-Shaw cell. Zbl 1382.76071Zhao, Meng; Belmonte, Andrew; Li, Shuwang; Li, Xiaofan; Lowengrub, John 5 2016 Nonlinear studies of tumor morphological stability using a two-fluid flow model. Zbl 1407.76031Pham, Kara; Turian, Emma; Liu, Kai; Li, Shuwang; Lowengrub, John 4 2018 The effects of cell compressibility, motility and contact inhibition on the growth of tumor cell clusters using the cellular Potts model. Zbl 1411.92140Li, Jonathan F.; Lowengrub, John 4 2014 The convergence of an exact desingularization for vortex methods. Zbl 0769.76045Hou, T. Y.; Lowengrub, J.; Shelley, M. J. 4 1993 A diffuse domain method for two-phase flows with large density ratio in complex geometries. Zbl 1461.76447Guo, Zhenlin; Yu, Fei; Lin, Ping; Wise, Steven; Lowengrub, John 4 2021 Nonlinear simulation of the effect of microenvironment on tumor growth. Zbl 1451.92102Macklin, Paul; Lowengrub, John 4 2007 The effect of spontaneous curvature on a two-phase vesicle. Zbl 1325.92028Cox, Geoffrey; Lowengrub, John 4 2015 Locomotion, wrinkling, and budding of a multicomponent vesicle in viscous fluids. Zbl 1282.35420Li, Shuwang; Lowengrub, John; Voigt, Axel 4 2012 Almost optimal convergence of the point vortex method for vortex sheets using numerical filtering. Zbl 0935.76068Caflisch, Russel E.; Hou, Thomas Y.; Lowengrub, John 3 1999 Higher-order accurate diffuse-domain methods for partial differential equations with Dirichlet boundary conditions in complex, evolving geometries. Zbl 1453.65306Yu, Fei; Guo, Zhenlin; Lowengrub, John 3 2020 An efficient rescaling algorithm for simulating the evolution of multiple elastically stressed precipitates. Zbl 1373.74079Barua, Amlan K.; Li, Shuwang; Feng, Hualong; Li, Xiaofan; Lowengrub, John 3 2013 Axisymmetric multicomponent vesicles: a comparison of hydrodynamic and geometric models. Zbl 1310.92018Sohn, Jinsun; Li, Shuwang; Li, Xiaofan; Lowengrub, John S. 3 2012 Three-dimensional spatiotemporal modeling of colon cancer organoids reveals that multimodal control of stem cell self-renewal is a critical determinant of size and shape in early stages of tumor growth. Zbl 1394.92068Yan, Huaming; Konstorum, Anna; Lowengrub, John S. 2 2018 Exact desingularization and local regridding for vortex methods. Zbl 0825.76647Hou, T. Y.; Lowengrub, J.; Shelley, M. J. 2 1991 Energy stable multigrid method for local and non-local hydrodynamic models for freezing. Zbl 1423.80022Baskaran, Arvind; Guan, Zhen; Lowengrub, John 2 2016 Stability of boundary integral methods for water waves. Zbl 0885.35095Beale, J. Thomas; Hou, Thomas Y.; Lowengrub, John 2 1997 An efficient adaptive rescaling scheme for computing moving interface problems. Zbl 1490.76088Zhao, Meng; Ying, Wenjun; Lowengrub, John; Li, Shuwang 2 2017 Boundary integral methods for dispersive equations, Airy flow and the modified Korteweg de Vries equation. Zbl 1422.65241Franco-de-Leon, Mariano; Lowengrub, John 1 2019 Efficient simulation of thermally fluctuating biopolymers immersed in fluids on 1-micron, 1-second scales. Zbl 1452.74038Liu, Kai; Lowengrub, John; Allard, Jun 1 2019 Nonlinear limiting dynamics of a shrinking interface in a Hele-Shaw cell. Zbl 1461.76143Zhao, Meng; Niroobakhsh, Zahra; Lowengrub, John; Li, Shuwang 1 2021 Tumor growth and calcification in evolving microenvironmental geometries. Zbl 1406.92287Chen, Ying; Lowengrub, John S. 1 2019 Complex far-field geometries determine the stability of solid tumor growth with chemotaxis. Zbl 1439.92044Lu, Min-Jhe; Liu, Chun; Lowengrub, John; Li, Shuwang 1 2020 Second order approximation for a quasi-incompressible Navier-Stokes Cahn-Hilliard system of two-phase flows with variable density. Zbl 07516811Guo, Zhenlin; Cheng, Qing; Lin, Ping; Liu, Chun; Lowengrub, John 1 2022 Morphological stability of an elastic tumor-host interface. Zbl 1451.74171Turian, Emma; Liu, Kai; Lowengrub, John; Li, Shuwang 1 2019 Second order approximation for a quasi-incompressible Navier-Stokes Cahn-Hilliard system of two-phase flows with variable density. Zbl 07516811Guo, Zhenlin; Cheng, Qing; Lin, Ping; Liu, Chun; Lowengrub, John 1 2022 A diffuse domain method for two-phase flows with large density ratio in complex geometries. Zbl 1461.76447Guo, Zhenlin; Yu, Fei; Lin, Ping; Wise, Steven; Lowengrub, John 4 2021 Nonlinear limiting dynamics of a shrinking interface in a Hele-Shaw cell. Zbl 1461.76143Zhao, Meng; Niroobakhsh, Zahra; Lowengrub, John; Li, Shuwang 1 2021 A multiscale model of virus pandemic: heterogeneous interactive entities in a globally connected world. Zbl 1451.92276Bellomo, Nicola; Bingham, Richard; Chaplain, Mark A. J.; Dosi, Giovanni; Forni, Guido; Knopoff, Damian A.; Lowengrub, John; Twarock, Reidun; Virgillito, Maria Enrica 37 2020 Higher-order accurate diffuse-domain methods for partial differential equations with Dirichlet boundary conditions in complex, evolving geometries. Zbl 1453.65306Yu, Fei; Guo, Zhenlin; Lowengrub, John 3 2020 Complex far-field geometries determine the stability of solid tumor growth with chemotaxis. Zbl 1439.92044Lu, Min-Jhe; Liu, Chun; Lowengrub, John; Li, Shuwang 1 2020 Boundary integral methods for dispersive equations, Airy flow and the modified Korteweg de Vries equation. Zbl 1422.65241Franco-de-Leon, Mariano; Lowengrub, John 1 2019 Efficient simulation of thermally fluctuating biopolymers immersed in fluids on 1-micron, 1-second scales. Zbl 1452.74038Liu, Kai; Lowengrub, John; Allard, Jun 1 2019 Tumor growth and calcification in evolving microenvironmental geometries. Zbl 1406.92287Chen, Ying; Lowengrub, John S. 1 2019 Morphological stability of an elastic tumor-host interface. Zbl 1451.74171Turian, Emma; Liu, Kai; Lowengrub, John; Li, Shuwang 1 2019 A uniquely solvable, energy stable numerical scheme for the functionalized Cahn-Hilliard equation and its convergence analysis. Zbl 1398.65208Feng, Wenqiang; Guan, Zhen; Lowengrub, John; Wang, Cheng; Wise, Steven M.; Chen, Ying 24 2018 Efficient energy stable schemes for isotropic and strongly anisotropic Cahn-Hilliard systems with the Willmore regularization. Zbl 1395.65014Chen, Ying; Lowengrub, John; Shen, Jie; Wang, Cheng; Wise, Steven 20 2018 A mass-conservative adaptive FAS multigrid solver for cell-centered finite difference methods on block-structured, locally-Cartesian grids. Zbl 1380.65402Feng, Wenqiang; Guo, Zhenlin; Lowengrub, John S.; Wise, Steven M. 17 2018 Computation of a shrinking interface in a Hele-Shaw cell. Zbl 1396.76029Zhao, Meng; Li, Xiaofan; Ying, Wenjun; Belmonte, Andrew; Lowengrub, John; Li, Shuwang 7 2018 Nonlinear studies of tumor morphological stability using a two-fluid flow model. Zbl 1407.76031Pham, Kara; Turian, Emma; Liu, Kai; Li, Shuwang; Lowengrub, John 4 2018 Three-dimensional spatiotemporal modeling of colon cancer organoids reveals that multimodal control of stem cell self-renewal is a critical determinant of size and shape in early stages of tumor growth. Zbl 1394.92068Yan, Huaming; Konstorum, Anna; Lowengrub, John S. 2 2018 Convergence analysis for second-order accurate schemes for the periodic nonlocal Allen-Cahn and Cahn-Hilliard equations. Zbl 1387.65087Guan, Zhen; Lowengrub, John; Wang, Cheng 31 2017 Mass conservative and energy stable finite difference methods for the quasi-incompressible Navier-Stokes-Cahn-Hilliard system: primitive variable and projection-type schemes. Zbl 1439.76121Guo, Z.; Lin, P.; Lowengrub, J.; Wise, S. M. 25 2017 An efficient adaptive rescaling scheme for computing moving interface problems. Zbl 1490.76088Zhao, Meng; Ying, Wenjun; Lowengrub, John; Li, Shuwang 2 2017 Feedback regulation in a cancer stem cell model can cause an Allee effect. Zbl 1341.92029Konstorum, Anna; Hillen, Thomas; Lowengrub, John 9 2016 Numerical simulation of endocytosis: viscous flow driven by membranes with non-uniformly distributed curvature-inducing molecules. Zbl 1351.76067Lowengrub, John; Allard, Jun; Aland, Sebastian 8 2016 An interface-fitted adaptive mesh method for elliptic problems and its application in free interface problems with surface tension. Zbl 1357.65271Zheng, Xiaoming; Lowengrub, John 7 2016 An energy stable, hexagonal finite difference scheme for the 2D phase field crystal amplitude equations. Zbl 1349.74360Guan, Zhen; Heinonen, Vili; Lowengrub, John; Wang, Cheng; Wise, Steven M. 7 2016 Nonlinear simulations of elastic fingering in a Hele-Shaw cell. Zbl 1382.76071Zhao, Meng; Belmonte, Andrew; Li, Shuwang; Li, Xiaofan; Lowengrub, John 5 2016 Energy stable multigrid method for local and non-local hydrodynamic models for freezing. Zbl 1423.80022Baskaran, Arvind; Guan, Zhen; Lowengrub, John 2 2016 Analysis of the diffuse-domain method for solving PDEs in complex geometries. Zbl 1328.65223Lervåg, Karl Yngve; Lowengrub, John 11 2015 The effect of spontaneous curvature on a two-phase vesicle. Zbl 1325.92028Cox, Geoffrey; Lowengrub, John 4 2015 Second order convex splitting schemes for periodic nonlocal Cahn-Hilliard and Allen-Cahn equations. Zbl 1349.65298Guan, Zhen; Lowengrub, John S.; Wang, Cheng; Wise, Steven M. 83 2014 A numerical method for the quasi-incompressible Cahn-Hilliard-Navier-Stokes equations for variable density flows with a discrete energy law. Zbl 1349.76057Guo, Z.; Lin, P.; Lowengrub, J. S. 41 2014 Diffuse interface models of locally inextensible vesicles in a viscous fluid. Zbl 1349.76933Aland, Sebastian; Egerer, Sabine; Lowengrub, John; Voigt, Axel 32 2014 Tumor growth in complex, evolving microenvironmental geometries: a diffuse domain approach. Zbl 1303.92042Chen, Ying; Lowengrub, John S. 7 2014 The effects of cell compressibility, motility and contact inhibition on the growth of tumor cell clusters using the cellular Potts model. Zbl 1411.92140Li, Jonathan F.; Lowengrub, John 4 2014 Convergence analysis of a second order convex splitting scheme for the modified phase field crystal equation. Zbl 1401.82046Baskaran, A.; Lowengrub, J. S.; Wang, C.; Wise, S. M. 96 2013 Energy stable and efficient finite-difference nonlinear multigrid schemes for the modified phase field crystal equation. Zbl 1349.65265Baskaran, Arvind; Hu, Zhengzheng; Lowengrub, John S.; Wang, Cheng; Wise, Steven M.; Zhou, Peng 72 2013 Analysis of a mixture model of tumor growth. Zbl 1292.35153Lowengrub, John; Titi, Edriss; Zhao, Kun 40 2013 The effect of interstitial pressure on tumor growth: coupling with the blood and lymphatic vascular systems. Zbl 1406.92330Wu, Min; Frieboes, Hermann B.; McDougall, Steven R.; Chaplain, Mark A. J.; Cristini, Vittorio; Lowengrub, John 10 2013 Thermodynamically consistent models for two-component vesicles. Zbl 1306.92014Haußer, Frank; Marth, Wieland; Li, Shuwang; Lowengrub, John; Rätz, Andreas; Voigt, Axel 5 2013 An efficient rescaling algorithm for simulating the evolution of multiple elastically stressed precipitates. Zbl 1373.74079Barua, Amlan K.; Li, Shuwang; Feng, Hualong; Li, Xiaofan; Lowengrub, John 3 2013 Multispecies model of cell lineages and feedback control in solid tumors. Zbl 1397.92381Youssefpour, H.; Li, X.; Lander, A. D.; Lowengrub, J. S. 14 2012 Density-dependent quiescence in glioma invasion: instability in a simple reaction-diffusion model for the migration/proliferation dichotomy. Zbl 1448.92064Pham, Kara; Chauviere, Arnaud; Hatzikirou, Haralambos; Li, Xiangrong; Byrne, Helen M.; Cristini, Vittorio; Lowengrub, John 6 2012 Modeling an elastic fingering instability in a reactive Hele-Shaw flow. Zbl 1343.76011He, Ong; Lowengrub, John; Belmonte, Andrew 6 2012 Locomotion, wrinkling, and budding of a multicomponent vesicle in viscous fluids. Zbl 1282.35420Li, Shuwang; Lowengrub, John; Voigt, Axel 4 2012 Axisymmetric multicomponent vesicles: a comparison of hydrodynamic and geometric models. Zbl 1310.92018Sohn, Jinsun; Li, Shuwang; Li, Xiaofan; Lowengrub, John S. 3 2012 A diffuse-interface method for two-phase flows with soluble surfactants. Zbl 1428.76210Teigen, Knut Erik; Song, Peng; Lowengrub, John; Voigt, Axel 75 2011 An adaptive multigrid algorithm for simulating solid tumor growth using mixture models. Zbl 1211.65123Wise, S. M.; Lowengrub, J. S.; Cristini, V. 45 2011 A grid based particle method for solving partial differential equations on evolving surfaces and modeling high order geometrical motion. Zbl 1316.65089Leung, Shingyu; Lowengrub, John; Zhao, Hongkai 36 2011 A continuum model of colloid-stabilized interfaces. Zbl 1308.76159Aland, Sebastian; Lowengrub, John; Voigt, Axel 10 2011 Numerical study of surfactant-laden drop-drop interactions. Zbl 1364.76165Xu, Jian-Jun; Li, Zhilin; Lowengrub, John; Zhao, Hongkai 8 2011 Nonlinear modelling of cancer: bridging the gap between cells and tumours. Zbl 1181.92046Lowengrub, J. S.; Frieboes, H. B.; Jin, F.; Chuang, Y-L; Li, X.; Macklin, P.; Wise, S. M.; Cristini, V. 140 2010 Three-dimensional multispecies nonlinear tumor growth. II: Tumor invasion and angiogenesis. Zbl 1406.92049Frieboes, Hermann B.; Jin, Fang; Chuang, Yao-Li; Wise, Steven M.; Lowengrub, John S.; Cristini, Vittorio 43 2010 Two-phase flow in complex geometries: a diffuse domain approach. Zbl 1231.76200Aland, S.; Lowengrub, J.; Voigt, A. 24 2010 Dynamics of multicomponent vesicles in a viscous fluid. Zbl 1381.76053Sohn, Jin Sun; Tseng, Yu-Hau; Li, Shuwang; Voigt, Axel; Lowengrub, John S. 22 2010 An energy-stable and convergent finite-difference scheme for the phase field crystal equation. Zbl 1201.35027Wise, S. M.; Wang, Cheng; Lowengrub, J. S. 223 2009 Stable and efficient finite-difference nonlinear-multigrid schemes for the phase field crystal equation. Zbl 1171.82015Hu, Z.; Wise, S. M.; Wang, C.; Lowengrub, J. S. 171 2009 Nonlinear simulations of solid tumor growth using a mixture model: invasion and branching. Zbl 1311.92039Cristini, Vittorio; Li, Xiangrong; Lowengrub, John S.; Wise, Steven M. 107 2009 Multiscale modelling and nonlinear simulation of vascular tumour growth. Zbl 1311.92040Macklin, Paul; McDougall, Steven; Anderson, Alexander R. A.; Chaplain, Mark A. J.; Cristini, Vittorio; Lowengrub, John 73 2009 Solving PDEs in complex geometries: a diffuse domain approach. Zbl 1178.35027Li, X.; Lowengrub, J.; Rätz, A.; Voigt, A. 67 2009 A new phase-field model for strongly anisotropic systems. Zbl 1186.80014Torabi, Solmaz; Lowengrub, John; Voigt, Axel; Wise, Steven 61 2009 A diffuse-interface approach for modelling transport, diffusion and adsorption/desorption of material quantities on a deformable interface. Zbl 1186.35168Teigen, Knut Erik; Li, Xiangrong; Lowengrub, John; Wang, Fan; Voigt, Axel 44 2009 Geometric evolution laws for thin crystalline films: modeling and numerics. Zbl 1364.74062Li, Bo; Lowengrub, John; Ratz, Andreas; Voigt, Axel 15 2009 Three-dimensional multispecies nonlinear tumor growth. I: Model and numerical method. Zbl 1398.92135Wise, S. M.; Lowengrub, J. S.; Frieboes, H. B.; Cristini, Vittorio 154 2008 A new ghost cell/level set method for moving boundary problems: application to tumor growth. Zbl 1203.65144Macklin, Paul; Lowengrub, John S. 25 2008 Solving the regularized, strongly anisotropic Cahn-Hilliard equation by an adaptive nonlinear multigrid method. Zbl 1310.82044Wise, Steven; Kim, Junseok; Lowengrub, John 84 2007 Nonlinear three-dimensional simulation of solid tumor growth. Zbl 1124.92022Li, Xiangrong; Cristini, Vittorio; Nie, Qing; Lowengrub, John S. 19 2007 A rescaling scheme with application to the long-time simulation of viscous fingering in a Hele-Shaw cell. Zbl 1343.76048Li, Shuwang; Lowengrub, John S.; Leo, Perry H. 18 2007 Surface phase separation and flow in a simple model of multicomponent drops and vesicles. Zbl 1153.76441Lowengrub, J. S.; Xu, J-J.; Voigt, A. 9 2007 Nonlinear simulation of the effect of microenvironment on tumor growth. Zbl 1451.92102Macklin, Paul; Lowengrub, John 4 2007 A level-set method for interfacial flows with surfactant. Zbl 1161.76548Xu, Jian-Jun; Li, Zhilin; Lowengrub, John; Zhao, Hongkai 81 2006 An adaptive coupled level-set/volume-of-fluid interface capturing method for unstructured triangular grids. Zbl 1160.76377Yang, Xiaofeng; James, Ashley J.; Lowengrub, John; Zheng, Xiaoming; Cristini, Vittorio 51 2006 An improved geometry-aware curvature discretization for level set methods: Application to tumor growth. Zbl 1089.92024Macklin, Paul; Lowengrub, John 31 2006 Numerical evidence of nonuniqueness in the evolution of vortex sheets. Zbl 1124.76010Lopes Filho, Milton C.; Lowengrub, John; Nussenzveig Lopes, Helena J.; Zheng, Yuxi 22 2006 Phase field modeling and simulation of three-phase flows. Zbl 1100.35088Kim, Junseok; Lowengrub, John 68 2005 Evolving interfaces via gradients of geometry-dependent interior Poisson problems: application to tumor growth. Zbl 1067.65111Macklin, Paul; Lowengrub, John 38 2005 Adaptive unstructured volume remeshing. II: Application to two- and three-dimensional level-set simulations of multiphase flow. Zbl 1075.65120Zheng, Xiaoming; Lowengrub, John; Anderson, Anthony; Cristini, Vittorio 36 2005 Conservative multigrid methods for Cahn–Hilliard fluids. Zbl 1109.76348Kim, Junseok; Kang, Kyungkeun; Lowengrub, John 134 2004 A surfactant-conserving volume-of-fluid method for interfacial flows with insoluble surfactant. Zbl 1061.76062James, Ashley J.; Lowengrub, John 79 2004 Conservative multigrid methods for ternary Cahn-Hilliard systems. Zbl 1085.65093Kim, Junseok; Kang, Kyungkeun; Lowengrub, John 37 2004 Nonlinear simulation of tumor growth. Zbl 1023.92013Cristini, Vittorio; Lowengrub, John; Nie, Qing 97 2003 Modeling pinchoff and reconnection in a Hele-Shaw cell. I: The models and their calibration. Zbl 1184.76316Lee, Hyeong-Gi; Lowengrub, J. S.; Goodman, J. 61 2002 Modeling pinchoff and reconnection in a Hele-Shaw cell. II: Analysis and simulation in the nonlinear regime. Zbl 1184.76317Lee, Hyeong-Gi; Lowengrub, J. S.; Goodman, J. 53 2002 Boundary integral methods for multicomponent fluids and multiphase materials. Zbl 1046.76029Hou, T. Y.; Lowengrub, J. S.; Shelley, M. J. 66 2001 Focusing of an elongated hole in porous medium flow. Zbl 0989.35082Angenent, S. B.; Aronson, D. G.; Betelu, S. I.; Lowengrub, J. S. 10 2001 Microstructural evolution in orthotropic elastic media. Zbl 0960.74076Leo, P. H.; Lowengrub, J. S.; Nie, Qing 19 2000 Topological transitions in liquid/liquid interfaces. Zbl 0929.35191Lowengrub, J. S.; Goodman, J.; Lee, H.; Longmire, E. K.; Shelley, M. J.; Truskinovsky, L. 7 1999 Almost optimal convergence of the point vortex method for vortex sheets using numerical filtering. Zbl 0935.76068Caflisch, Russel E.; Hou, Thomas Y.; Lowengrub, John 3 1999 Quasi-incompressible Cahn-Hilliard fluids and topological transitions. Zbl 0927.76007Lowengrub, J.; Truskinovsky, L. 325 1998 The long-time motion of vortex sheets with surface tension. Zbl 1185.76545Hou, T. Y.; Lowengrub, J. S.; Shelly, M. J. 67 1997 Microstructural evolution in inhomogeneous elastic media. Zbl 0880.73050Jou, H.-J.; Leo, P. H.; Lowengrub, J. S. 43 1997 Stability of boundary integral methods for water waves. Zbl 0885.35095Beale, J. Thomas; Hou, Thomas Y.; Lowengrub, John 2 1997 Convergence of a boundary integral method for water waves. Zbl 0858.76046Beale, J. Thomas; Hou, Thomas Y.; Lowengrub, John 32 1996 Removing the stiffness from interfacial flows with surface tension. Zbl 0810.76095Hou, Thomas Y.; Lowengrub, John S.; Shelley, Michael J. 205 1994 Spatial and temporal stability issues for interfacial flows with surface tension. Zbl 0816.76050Beale, J. T.; Hou, T. Y.; Lowengrub, J. S.; Shelley, M. J. 7 1994 Growth rates for the linearized motion of fluid interfaces away from equilibrium. Zbl 0796.76041Beale, J. Thomas; Hou, Thomas Y.; Lowengrub, John S. 62 1993 High-order and efficient methods for the vorticity formulation of the Euler equations. Zbl 0815.76068Lowengrub, J. S.; Shelley, M. J.; Merriman, B. 11 1993 The convergence of an exact desingularization for vortex methods. Zbl 0769.76045Hou, T. Y.; Lowengrub, J.; Shelley, M. J. 4 1993 Convergence of a point vortex method for vortex sheets. Zbl 0799.76062Hou, Thomas Y.; Lowengrub, John; Krasny, Robert 9 1991 Exact desingularization and local regridding for vortex methods. Zbl 0825.76647Hou, T. Y.; Lowengrub, J.; Shelley, M. J. 2 1991 Convergence of the point vortex method for the 2-D Euler equations. Zbl 0694.76013Goodman, Jonathan; Hou, Thomas Y.; Lowengrub, John 47 1990 Convergence of the point vortex method for the 3-D Euler equations. Zbl 0856.76059Hou, Thomas Y.; Lowengrub, John 12 1990 Convergence of the vortex method for vortex sheets. Zbl 0676.76023Caflisch, Russel E.; Lowengrub, John S. 15 1989 all cited Publications top 5 cited Publications all top 5 Cited by 2,770 Authors 68 Lowengrub, John Samuel 67 Kim, Junseok 60 Yang, Xiaofeng 49 Wang, Cheng 46 Wise, Steven M. 37 Garcke, Harald 29 Li, Yibao 28 Yang, Junxiang 27 Wang, Qi 24 Lee, Hyun Geun 24 Zhao, Jia 22 Liu, Chun 22 Shen, Jie 20 Grasselli, Maurizio 19 Miranville, Alain M. 19 Nürnberg, Robert 19 Voigt, Axel 18 Chen, Wenbin 17 Gómez, Héctor J. 17 Lam, Kei Fong 17 Li, Shuwang 16 Ambrose, David M. 16 Gancedo, Francisco 16 Han, Daozhi 16 Rocca, Elisabetta 15 Chaplain, Mark A. J. 15 Du, Qiang 15 Hou, Thomas Yizhao 15 Kou, Jisheng 15 Wang, Xiaoming 15 Zhang, Zhengru 14 Jeong, Darae 14 Oden, John Tinsley 14 Qiao, Zhonghua 14 Shelley, Michael J. 14 Shin, Jaemin 14 Wu, Hao 13 Ceniceros, Hector D. 13 Cordoba, Diego 13 Cristini, Vittorio 13 Zhang, Jun 12 Barrett, John William 12 Colli, Pierluigi 12 Giorgini, Andrea 12 Lai, Mingchih 12 Lee, Chaeyoung 12 Perthame, Benoît 12 Signori, Andrea 12 Sun, Shuyu 11 Abels, Helmut 11 Dehghan Takht Fooladi, Mehdi 11 Jia, Hongen 11 Li, Xiao 11 Li, Zhilin 10 Byrne, Helen Mary 10 Hu, Bei 10 Ju, Lili 10 Lin, Ping 10 Nie, Qing 10 Zhang, Hui 9 Aland, Sebastian 9 Cheng, Kelong 9 Feng, Xinlong 9 Gal, Ciprian Gheorghe Sorin 9 Hao, Wenrui 9 He, Xiaoming 9 Kahle, Christian 9 Lee, June-Yub 9 Li, Xiaoli 9 Sprekels, Jürgen 9 Walker, Shawn W. 9 Zheng, Xiaoming 8 Anderson, Alexander R. A. 8 Chen, Chuanjun 8 Choi, Yongho 8 Feng, Wenqiang 8 Frieboes, Hermann B. 8 Gong, Yuezheng 8 Kotschote, Matthias 8 Lima, Ernesto A. B. F. 8 Lorenzi, Tommaso 8 Mikula, Karol 8 Nochetto, Ricardo Horacio 8 Siegel, Michael 8 van der Zee, Kristoffer George 8 Wang, Liqun 8 Wang, Xiuhua 8 Xu, Yan 8 Yang, Jiang 7 Beale, J. Thomas 7 Fabrizio, Mauro 7 Frigeri, Sergio 7 Guo, Ruihan 7 Guo, Zhenlin 7 Helsing, Johan 7 Hou, Songming 7 Jabin, Pierre-Emmanuel 7 Lee, Seunggyu Lee 7 Liu, Zhengguang 7 Mauri, Roberto ...and 2,670 more Authors all top 5 Cited in 232 Serials 377 Journal of Computational Physics 85 Computer Methods in Applied Mechanics and Engineering 71 Journal of Scientific Computing 64 M\(^3\)AS. Mathematical Models & Methods in Applied Sciences 63 Journal of Theoretical Biology 58 Journal of Computational and Applied Mathematics 55 Journal of Fluid Mechanics 51 Computers and Fluids 51 Computers & Mathematics with Applications 46 Physics of Fluids 40 SIAM Journal on Scientific Computing 35 Applied Numerical Mathematics 32 Communications in Computational Physics 31 Bulletin of Mathematical Biology 30 Journal of Mathematical Biology 24 Mathematics of Computation 22 SIAM Journal on Numerical Analysis 21 Journal of Differential Equations 18 Archive for Rational Mechanics and Analysis 18 Physica D 17 Applied Mathematics and Computation 17 Numerische Mathematik 17 Advances in Computational Mathematics 17 Communications in Nonlinear Science and Numerical Simulation 16 Discrete and Continuous Dynamical Systems. Series B 15 European Journal of Applied Mathematics 15 Engineering Analysis with Boundary Elements 14 Applied Mathematics Letters 14 European Journal of Mechanics. B. Fluids 14 Nonlinear Analysis. Real World Applications 14 European Series in Applied and Industrial Mathematics (ESAIM): Mathematical Modelling and Numerical Analysis 14 Advances in Applied Mathematics and Mechanics 13 Mathematical Methods in the Applied Sciences 13 Applied Mathematics and Optimization 13 Mathematical Biosciences and Engineering 13 Discrete and Continuous Dynamical Systems. Series S 12 SIAM Journal on Mathematical Analysis 12 Journal of Nonlinear Science 11 Mathematics and Computers in Simulation 11 Applied Mathematical Modelling 11 SIAM Journal on Applied Mathematics 11 Discrete and Continuous Dynamical Systems 10 International Journal for Numerical Methods in Fluids 10 Journal of Engineering Mathematics 10 Journal of Mathematical Analysis and Applications 10 Annales de l’Institut Henri Poincaré. Analyse Non Linéaire 9 Communications in Mathematical Physics 9 ZAMP. Zeitschrift für angewandte Mathematik und Physik 9 Computational and Applied Mathematics 9 Multiscale Modeling & Simulation 8 Journal of the Mechanics and Physics of Solids 8 Nonlinearity 8 Journal of Mathematical Fluid Mechanics 7 Physica A 7 Computational Mechanics 7 Numerical Methods for Partial Differential Equations 7 Numerical Algorithms 7 Mathematical Problems in Engineering 7 Interfaces and Free Boundaries 7 Archives of Computational Methods in Engineering 6 Applicable Analysis 6 Communications in Partial Differential Equations 6 Calculus of Variations and Partial Differential Equations 6 Computing and Visualization in Science 6 Communications on Pure and Applied Analysis 6 East Asian Journal on Applied Mathematics 6 AIMS Mathematics 5 Journal of Functional Analysis 5 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods 5 Quarterly of Applied Mathematics 5 Chinese Annals of Mathematics. Series B 5 European Series in Applied and Industrial Mathematics (ESAIM): Control, Optimization and Calculus of Variations 5 Networks and Heterogeneous Media 5 Mathematical Modelling of Natural Phenomena 4 International Journal of Engineering Science 4 Journal of Statistical Physics 4 BIT 4 International Journal for Numerical Methods in Engineering 4 Inventiones Mathematicae 4 Journal of the American Mathematical Society 4 Asymptotic Analysis 4 Proceedings of the National Academy of Sciences of the United States of America 4 SIAM Review 4 Annals of Mathematics. Second Series 4 Computational Geosciences 4 The ANZIAM Journal 4 International Journal of Numerical Analysis and Modeling 4 Philosophical Transactions of the Royal Society of London. A. Mathematical, Physical and Engineering Sciences 3 Communications on Pure and Applied Mathematics 3 Journal of Mathematical Physics 3 Chaos, Solitons and Fractals 3 SIAM Journal on Control and Optimization 3 Mathematical and Computer Modelling 3 Japan Journal of Industrial and Applied Mathematics 3 Journal de Mathématiques Pures et Appliquées. Neuvième Série 3 Journal of Dynamics and Differential Equations 3 Continuum Mechanics and Thermodynamics 3 Russian Journal of Numerical Analysis and Mathematical Modelling 3 Mathematics and Mechanics of Solids 3 Living Reviews in Relativity ...and 132 more Serials all top 5 Cited in 39 Fields 1,001 Fluid mechanics (76-XX) 973 Partial differential equations (35-XX) 944 Numerical analysis (65-XX) 433 Biology and other natural sciences (92-XX) 207 Mechanics of deformable solids (74-XX) 159 Statistical mechanics, structure of matter (82-XX) 72 Classical thermodynamics, heat transfer (80-XX) 63 Calculus of variations and optimal control; optimization (49-XX) 40 Dynamical systems and ergodic theory (37-XX) 34 Probability theory and stochastic processes (60-XX) 23 Global analysis, analysis on manifolds (58-XX) 21 Computer science (68-XX) 21 Geophysics (86-XX) 20 Integral equations (45-XX) 18 Ordinary differential equations (34-XX) 17 Optics, electromagnetic theory (78-XX) 16 Differential geometry (53-XX) 13 Statistics (62-XX) 9 Real functions (26-XX) 9 Mechanics of particles and systems (70-XX) 9 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 6 Approximations and expansions (41-XX) 6 Operator theory (47-XX) 6 Systems theory; control (93-XX) 5 Quantum theory (81-XX) 4 Functions of a complex variable (30-XX) 4 Operations research, mathematical programming (90-XX) 3 General and overarching topics; collections (00-XX) 3 Harmonic analysis on Euclidean spaces (42-XX) 3 Relativity and gravitational theory (83-XX) 3 Information and communication theory, circuits (94-XX) 2 Linear and multilinear algebra; matrix theory (15-XX) 2 Measure and integration (28-XX) 2 Difference and functional equations (39-XX) 2 Functional analysis (46-XX) 1 Algebraic geometry (14-XX) 1 Potential theory (31-XX) 1 Integral transforms, operational calculus (44-XX) 1 Mathematics education (97-XX) Citations by Year