Edit Profile (opens in new tab) Towers, John D. Co-Author Distance Author ID: towers.john-d Published as: Towers, John D.; Towers, J. D. Documents Indexed: 44 Publications since 2000, including 3 Additional arXiv Preprints Co-Authors: 8 Co-Authors with 28 Joint Publications 254 Co-Co-Authors all top 5 Co-Authors 16 single-authored 23 Karlsen, Kenneth Hvistendahl 15 Bürger, Raimund 7 Risebro, Nils Henrik 5 Ghoshal, Shyam Sundar 4 Vaidya, Ganesh 1 Jana, Animesh 1 Mishra, Siddhartha 1 Torres, Héctor all top 5 Serials 6 Journal of Computational Physics 5 Numerische Mathematik 4 Journal of Hyperbolic Differential Equations 4 Networks and Heterogeneous Media 3 SIAM Journal on Numerical Analysis 2 Journal of Engineering Mathematics 1 IMA Journal of Numerical Analysis 1 Journal of Differential Equations 1 Chinese Annals of Mathematics. Series B 1 Applied Numerical Mathematics 1 European Journal of Applied Mathematics 1 SIAM Journal on Applied Mathematics 1 Electronic Journal of Differential Equations (EJDE) 1 Skrifter. Det Kongelige Norske Videnskabers Selskab 1 Computing and Visualization in Science 1 Communications in Applied Mathematics and Computational Science 1 Scientia. Series A: Mathematical Sciences. New Series 1 PAMM. Proceedings in Applied Mathematics and Mechanics 1 Advances in Applied Mathematics and Mechanics all top 5 Fields 32 Numerical analysis (65-XX) 31 Partial differential equations (35-XX) 13 Fluid mechanics (76-XX) 4 Operations research, mathematical programming (90-XX) 3 Mechanics of deformable solids (74-XX) 2 Approximations and expansions (41-XX) 2 Functional analysis (46-XX) 1 Global analysis, analysis on manifolds (58-XX) 1 Classical thermodynamics, heat transfer (80-XX) 1 Statistical mechanics, structure of matter (82-XX) 1 Biology and other natural sciences (92-XX) Publications by Year all cited Publications top 5 cited Publications Citations contained in zbMATH Open 37 Publications have been cited 785 times in 278 Documents Cited by ▼ Year ▼ Convergence of a difference scheme for conservation laws with a discontinuous flux. Zbl 0972.65060 Towers, John D. 93 2000 \(L^1\) stability for entropy solutions of nonlinear degenerate parabolic convection-diffusion equations with discontinuous coefficients. Zbl 1036.35104 Karlsen, K. H.; Risebro, N. H.; Towers, J. D. 79 2003 Convergence of the Lax-Friedrichs scheme and stability for conservation laws with a discontinuous space-time dependent flux. Zbl 1112.65085 Karlsen, K. H.; Towers, J. D. 70 2004 Upwind difference approximations for degenerate parabolic convection-diffusion equations with a discontinuous coefficient. Zbl 1014.65073 Karlsen, K. H.; Risebro, N. H.; Towers, J. D. 65 2002 Well-posedness in \(BV_t\) and convergence of a difference scheme for continuous sedimentation in ideal clarifier-thickener units. Zbl 1053.76047 Bürger, R.; Karlsen, K. H.; Risebro, N. H.; Towers, J. D. 64 2004 An Engquist-Osher-type scheme for conservation laws with discontinuous flux adapted to flux connections. Zbl 1201.35022 Bürger, Raimund; Karlsen, Kenneth H.; Towers, John D. 53 2009 A difference scheme for conservation laws with a discontinuous flux: the nonconvex case. Zbl 1055.65104 Towers, John D. 46 2001 A model of continuous sedimentation of flocculated suspensions in clarifier-thickener units. Zbl 1089.76061 Bürger, Raimund; Karlsen, Kenneth H.; Towers, John D. 43 2005 A family of numerical schemes for kinematic flows with discontinuous flux. Zbl 1200.76126 Bürger, R.; García, A.; Karlsen, K. H.; Towers, J. D. 43 2008 Two methods for discretizing a delta function supported on a level set. Zbl 1115.65028 Towers, John D. 26 2007 On a nonlinear degenerate parabolic transport-diffusion equation with a discontinuous coefficient. Zbl 1015.35049 Karlsen, Kenneth H.; Risebro, Nils H.; Towers, John D. 19 2002 Monotone difference approximations for the simulation of clarifier-thickener units. Zbl 1299.76283 Bürger, R.; Karlsen, K. H.; Risebro, N. H.; Towers, J. D. 16 2004 Convergence of a Godunov scheme for conservation laws with a discontinuous flux lacking the crossing condition. Zbl 1380.65158 Karlsen, K. H.; Towers, J. D. 16 2017 Difference schemes, entropy solutions, and speedup impulse for an inhomogeneous kinematic traffic flow model. Zbl 1173.35586 Bürger, Raimund; García, Antonio; Karlsen, Kenneth H.; Towers, John D. 14 2008 Second-order schemes for conservation laws with discontinuous flux modelling clarifier-thickener units. Zbl 1204.65101 Bürger, Raimund; Karlsen, Kenneth H.; Torres, Héctor; Towers, John D. 13 2010 Finite difference methods for approximating Heaviside functions. Zbl 1171.65014 Towers, John D. 11 2008 A source term method for Poisson problems on irregular domains. Zbl 1422.65327 Towers, John D. 9 2018 On a model for continuous sedimentation in vessels with discontinuous cross-sectional area. Zbl 1059.76542 Bürger, R.; Karlsen, K. H.; Risebro, N. H.; Towers, J. D. 8 2003 Front tracking for scalar balance equations. Zbl 1053.35088 Karlsen, K. H.; Risebro, N. H.; Towers, J. D. 8 2004 On some difference schemes and entropy conditions for a class of multi-species kinematic flow models with discontinuous flux. Zbl 1263.76048 Bürger, Raimund; Karlsen, Kenneth H.; Towers, John D. 8 2010 A convergence rate theorem for finite difference approximations to delta functions. Zbl 1155.65016 Towers, John D. 8 2008 An existence result for conservation laws having BV spatial flux heterogeneities – without concavity. Zbl 1440.35213 Towers, John D. 7 2020 A conservation law with discontinuous flux modelling traffic flow with abruptly changing road surface conditions. Zbl 1186.35005 Bürger, Raimund; Karlsen, Kenneth H.; Towers, John D. 7 2009 On an extended clarifier-thickener model with singular source and sink terms. Zbl 1201.35130 Bürger, R.; Garcia, A.; Karlsen, K. H.; Towers, J. D. 7 2006 Convergence via OSLC of the Godunov scheme for a scalar conservation law with time and space flux discontinuities. Zbl 1395.65042 Towers, John D. 6 2018 Discretizing delta functions via finite differences and gradient normalization. Zbl 1167.65007 Towers, John D. 6 2009 Finite difference methods for discretizing singular source terms in a Poisson interface problem. Zbl 1216.65143 Towers, John D. 6 2010 Convergence of the Godunov scheme for a scalar conservation law with time and space discontinuities. Zbl 1406.35190 Towers, John D. 5 2018 A fixed grid, shifted stencil scheme for inviscid fluid-particle interaction. Zbl 06638248 Towers, John D. 5 2016 On conservation laws with discontinuous flux. Zbl 1076.76069 Bürger, Raimund; Karlsen, Kenneth H.; Mishra, Siddharta; Towers, John D. 5 2005 Convergence of a Godunov scheme to an Audusse-Perthame adapted entropy solution for conservation laws with BV spatial flux. Zbl 1451.65107 Ghoshal, Shyam Sundar; Jana, Animesh; Towers, John D. 5 2020 Closed-form and finite difference solutions to a population balance model of grinding mills. Zbl 1097.74045 Bürger, Raimund; Karlsen, Kenneth H.; Towers, John D. 3 2005 An explicit finite volume algorithm for vanishing viscosity solutions on a network. Zbl 1487.90206 Towers, John D. 3 2022 A Godunov type scheme and error estimates for scalar conservation laws with Panov-type discontinuous flux. Zbl 07549401 Ghoshal, Shyam Sundar; Towers, John D.; Vaidya, Ganesh 3 2022 Convergence of monotone schemes for conservation laws with zero-flux boundary conditions. Zbl 1488.65365 Karlsen, K. H.; Towers, J. D. 2 2017 A splitting algorithm for LWR traffic models with flux discontinuous in the unknown. Zbl 07508351 Towers, John D. 2 2020 The Lax-Friedrichs scheme for interaction between the inviscid Burgers equation and multiple particles. Zbl 1436.65112 Towers, John D. 1 2020 An explicit finite volume algorithm for vanishing viscosity solutions on a network. Zbl 1487.90206 Towers, John D. 3 2022 A Godunov type scheme and error estimates for scalar conservation laws with Panov-type discontinuous flux. Zbl 07549401 Ghoshal, Shyam Sundar; Towers, John D.; Vaidya, Ganesh 3 2022 An existence result for conservation laws having BV spatial flux heterogeneities – without concavity. Zbl 1440.35213 Towers, John D. 7 2020 Convergence of a Godunov scheme to an Audusse-Perthame adapted entropy solution for conservation laws with BV spatial flux. Zbl 1451.65107 Ghoshal, Shyam Sundar; Jana, Animesh; Towers, John D. 5 2020 A splitting algorithm for LWR traffic models with flux discontinuous in the unknown. Zbl 07508351 Towers, John D. 2 2020 The Lax-Friedrichs scheme for interaction between the inviscid Burgers equation and multiple particles. Zbl 1436.65112 Towers, John D. 1 2020 A source term method for Poisson problems on irregular domains. Zbl 1422.65327 Towers, John D. 9 2018 Convergence via OSLC of the Godunov scheme for a scalar conservation law with time and space flux discontinuities. Zbl 1395.65042 Towers, John D. 6 2018 Convergence of the Godunov scheme for a scalar conservation law with time and space discontinuities. Zbl 1406.35190 Towers, John D. 5 2018 Convergence of a Godunov scheme for conservation laws with a discontinuous flux lacking the crossing condition. Zbl 1380.65158 Karlsen, K. H.; Towers, J. D. 16 2017 Convergence of monotone schemes for conservation laws with zero-flux boundary conditions. Zbl 1488.65365 Karlsen, K. H.; Towers, J. D. 2 2017 A fixed grid, shifted stencil scheme for inviscid fluid-particle interaction. Zbl 06638248 Towers, John D. 5 2016 Second-order schemes for conservation laws with discontinuous flux modelling clarifier-thickener units. Zbl 1204.65101 Bürger, Raimund; Karlsen, Kenneth H.; Torres, Héctor; Towers, John D. 13 2010 On some difference schemes and entropy conditions for a class of multi-species kinematic flow models with discontinuous flux. Zbl 1263.76048 Bürger, Raimund; Karlsen, Kenneth H.; Towers, John D. 8 2010 Finite difference methods for discretizing singular source terms in a Poisson interface problem. Zbl 1216.65143 Towers, John D. 6 2010 An Engquist-Osher-type scheme for conservation laws with discontinuous flux adapted to flux connections. Zbl 1201.35022 Bürger, Raimund; Karlsen, Kenneth H.; Towers, John D. 53 2009 A conservation law with discontinuous flux modelling traffic flow with abruptly changing road surface conditions. Zbl 1186.35005 Bürger, Raimund; Karlsen, Kenneth H.; Towers, John D. 7 2009 Discretizing delta functions via finite differences and gradient normalization. Zbl 1167.65007 Towers, John D. 6 2009 A family of numerical schemes for kinematic flows with discontinuous flux. Zbl 1200.76126 Bürger, R.; García, A.; Karlsen, K. H.; Towers, J. D. 43 2008 Difference schemes, entropy solutions, and speedup impulse for an inhomogeneous kinematic traffic flow model. Zbl 1173.35586 Bürger, Raimund; García, Antonio; Karlsen, Kenneth H.; Towers, John D. 14 2008 Finite difference methods for approximating Heaviside functions. Zbl 1171.65014 Towers, John D. 11 2008 A convergence rate theorem for finite difference approximations to delta functions. Zbl 1155.65016 Towers, John D. 8 2008 Two methods for discretizing a delta function supported on a level set. Zbl 1115.65028 Towers, John D. 26 2007 On an extended clarifier-thickener model with singular source and sink terms. Zbl 1201.35130 Bürger, R.; Garcia, A.; Karlsen, K. H.; Towers, J. D. 7 2006 A model of continuous sedimentation of flocculated suspensions in clarifier-thickener units. Zbl 1089.76061 Bürger, Raimund; Karlsen, Kenneth H.; Towers, John D. 43 2005 On conservation laws with discontinuous flux. Zbl 1076.76069 Bürger, Raimund; Karlsen, Kenneth H.; Mishra, Siddharta; Towers, John D. 5 2005 Closed-form and finite difference solutions to a population balance model of grinding mills. Zbl 1097.74045 Bürger, Raimund; Karlsen, Kenneth H.; Towers, John D. 3 2005 Convergence of the Lax-Friedrichs scheme and stability for conservation laws with a discontinuous space-time dependent flux. Zbl 1112.65085 Karlsen, K. H.; Towers, J. D. 70 2004 Well-posedness in \(BV_t\) and convergence of a difference scheme for continuous sedimentation in ideal clarifier-thickener units. Zbl 1053.76047 Bürger, R.; Karlsen, K. H.; Risebro, N. H.; Towers, J. D. 64 2004 Monotone difference approximations for the simulation of clarifier-thickener units. Zbl 1299.76283 Bürger, R.; Karlsen, K. H.; Risebro, N. H.; Towers, J. D. 16 2004 Front tracking for scalar balance equations. Zbl 1053.35088 Karlsen, K. H.; Risebro, N. H.; Towers, J. D. 8 2004 \(L^1\) stability for entropy solutions of nonlinear degenerate parabolic convection-diffusion equations with discontinuous coefficients. Zbl 1036.35104 Karlsen, K. H.; Risebro, N. H.; Towers, J. D. 79 2003 On a model for continuous sedimentation in vessels with discontinuous cross-sectional area. Zbl 1059.76542 Bürger, R.; Karlsen, K. H.; Risebro, N. H.; Towers, J. D. 8 2003 Upwind difference approximations for degenerate parabolic convection-diffusion equations with a discontinuous coefficient. Zbl 1014.65073 Karlsen, K. H.; Risebro, N. H.; Towers, J. D. 65 2002 On a nonlinear degenerate parabolic transport-diffusion equation with a discontinuous coefficient. Zbl 1015.35049 Karlsen, Kenneth H.; Risebro, Nils H.; Towers, John D. 19 2002 A difference scheme for conservation laws with a discontinuous flux: the nonconvex case. Zbl 1055.65104 Towers, John D. 46 2001 Convergence of a difference scheme for conservation laws with a discontinuous flux. Zbl 0972.65060 Towers, John D. 93 2000 all cited Publications top 5 cited Publications all top 5 Cited by 335 Authors 35 Bürger, Raimund 22 Karlsen, Kenneth Hvistendahl 18 Towers, John D. 17 Risebro, Nils Henrik 16 Andreianov, Boris 15 Diehl, Stefan 11 Mishra, Siddhartha 10 Gowda, G. D. Veerappa 9 Adimurthi, A. 9 Goatin, Paola 8 Ghoshal, Shyam Sundar 8 Zhang, Peng 7 Wong, Sze Chun 6 Cancès, Clément 6 Coclite, Giuseppe Maria 6 Villada, Luis Miguel 5 Abreu, Eduardo 5 Careaga, Julio 5 Gibou, Frédéric 5 Klingenberg, Christian 5 Panov, Evgeniy Yu. 5 Sylla, Abraham 5 Wang, Guodong 4 Chiarello, Felisia Angela 4 Göttlich, Simone 4 Lu, Yunguang 4 Rosini, Massimiliano Daniele 4 Sepúlveda, Mauricio A. 4 Shen, Chun 3 Berres, Stefan 3 Chalons, Christophe 3 Choi, Keechoo 3 Guerra, Graziano 3 Koley, Ujjwal 3 Kröker, Ilja 3 Kublik, Catherine M. 3 Kumar Kenettinkara, Sudarshan 3 Lambert, Wanderson J. 3 Mitrovic, Darko 3 Pineda, Romel 3 Qiao, Dianliang 3 Rossi, Elena 3 Salac, David 3 Seaïd, Mohammed 3 Shen, Wen 3 Sun, Meina 3 Tsai, Yen-Hsi Richard 3 Vaidya, Ganesh 3 Vega, Carlos A. 3 Wen, Xin 3 Zhao, Shan 2 Acosta, Carlos Daniel 2 Aggarwal, Aekta 2 Amadori, Debora 2 Aniszewski, Wojciech 2 Badwaik, Jayesh 2 Briani, Maya 2 Bustos, Abel 2 Contreras, Harold Deivi 2 Coronel, Aníbal 2 Cristiani, Emiliano 2 Donadello, Carlotta 2 Dutta, Rajib 2 Egan, Raphael 2 Eymard, Robert 2 Farås, Sebastian 2 Ferraz, Paola 2 Festa, Adriano 2 Fjordholm, Ulrik Skre 2 Friedrich, Jan 2 Gosse, Laurent 2 Gwiazda, Piotr 2 Herty, Michael Matthias 2 Hilhorst, Danielle 2 Holden, Helge 2 Jerez, Silvia 2 Keimer, Alexander 2 Kolahdouz, Ebrahim M. 2 Krunić, Tanja 2 Kummer, Florian 2 Kunzinger, Michael 2 Lin, Zhiyang 2 Liu, Jianguo 2 Ma, Yanying 2 Martí, María Carmen 2 Mejía, Carlos E. 2 Min, Chohong 2 Müller, Björn 2 Musch, Markus 2 Nedeljkov, Marko 2 Oberlack, Martin 2 Pflug, Lukas 2 Piccoli, Benedetto 2 Ren, Yiming 2 Rodríguez Bermúdez, Panters 2 Rohde, Christian 2 Ruf, Adrian M. 2 Ruiz-Baier, Ricardo 2 Ruiz, Ricardo M. 2 Saad, Mazen ...and 235 more Authors all top 5 Cited in 85 Serials 35 Journal of Computational Physics 17 Networks and Heterogeneous Media 14 European Series in Applied and Industrial Mathematics (ESAIM): Mathematical Modelling and Numerical Analysis 13 Journal of Differential Equations 11 Journal of Hyperbolic Differential Equations 10 Journal of Engineering Mathematics 9 Numerische Mathematik 8 Mathematics of Computation 7 M\(^3\)AS. Mathematical Models & Methods in Applied Sciences 7 Applied Mathematical Modelling 6 Computers & Mathematics with Applications 6 Applied Numerical Mathematics 6 Journal of Scientific Computing 5 Applied Mathematics and Computation 5 Journal of Computational and Applied Mathematics 4 Archive for Rational Mechanics and Analysis 4 ZAMP. Zeitschrift für angewandte Mathematik und Physik 4 SIAM Journal on Numerical Analysis 4 Numerical Methods for Partial Differential Equations 4 Applied Mathematics Letters 4 SIAM Journal on Applied Mathematics 4 SIAM Journal on Mathematical Analysis 4 SIAM Journal on Scientific Computing 4 Computational Geosciences 3 Journal of Mathematical Analysis and Applications 3 International Journal for Numerical Methods in Engineering 2 Applicable Analysis 2 Computer Methods in Applied Mechanics and Engineering 2 Journal of Functional Analysis 2 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods 2 Transactions of the American Mathematical Society 2 Acta Applicandae Mathematicae 2 Journal of Mathematical Sciences (New York) 2 ZAMM. Zeitschrift für Angewandte Mathematik und Mechanik 2 Nonlinear Analysis. Real World Applications 2 Bulletin of the Brazilian Mathematical Society. New Series 2 Discrete and Continuous Dynamical Systems. Series S 2 European Series in Applied and Industrial Mathematics (ESAIM): Proceedings and Surveys 1 Classical and Quantum Gravity 1 Communications on Pure and Applied Mathematics 1 General Relativity and Gravitation 1 Israel Journal of Mathematics 1 Journal of Mathematical Physics 1 Journal of Statistical Physics 1 Mathematical Methods in the Applied Sciences 1 Physica A 1 Annales Universitatis Mariae Curie-Skłodowska. Sectio A. Mathematica 1 BIT 1 Calcolo 1 Journal of the London Mathematical Society. Second Series 1 Applied Mathematics and Mechanics. (English Edition) 1 Annales de l’Institut Henri Poincaré. Analyse Non Linéaire 1 Mathematical and Computer Modelling 1 European Journal of Applied Mathematics 1 Communications in Partial Differential Equations 1 Communications in Numerical Methods in Engineering 1 Computational and Applied Mathematics 1 NoDEA. Nonlinear Differential Equations and Applications 1 Engineering Analysis with Boundary Elements 1 Discrete and Continuous Dynamical Systems 1 Computing and Visualization in Science 1 European Series in Applied and Industrial Mathematics (ESAIM): Control, Optimization and Calculus of Variations 1 Vietnam Journal of Mathematics 1 M2AN. Mathematical Modelling and Numerical Analysis. ESAIM, European Series in Applied and Industrial Mathematics 1 Communications in Nonlinear Science and Numerical Simulation 1 Communications in Contemporary Mathematics 1 Journal of Evolution Equations 1 Acta Mathematica Scientia. Series B. (English Edition) 1 Comptes Rendus. Mathématique. Académie des Sciences, Paris 1 Central European Journal of Mathematics 1 Multiscale Modeling & Simulation 1 TEMA. Tendências em Matemática Aplicada e Computacional 1 Granular Matter 1 International Journal of Computational Methods 1 International Journal of Numerical Analysis and Modeling 1 Mathematical Biosciences and Engineering 1 Communications in Applied Mathematics and Computational Science 1 International Journal of Differential Equations 1 Advances in Applied Mathematics and Mechanics 1 Science China. Mathematics 1 Journal of the Korean Society for Industrial and Applied Mathematics 1 Communications in Applied and Industrial Mathematics 1 Research in the Mathematical Sciences 1 Journal of Elliptic and Parabolic Equations 1 International Journal on Finite Volumes all top 5 Cited in 28 Fields 199 Partial differential equations (35-XX) 167 Numerical analysis (65-XX) 104 Fluid mechanics (76-XX) 39 Operations research, mathematical programming (90-XX) 8 Statistical mechanics, structure of matter (82-XX) 8 Biology and other natural sciences (92-XX) 7 Probability theory and stochastic processes (60-XX) 6 Mechanics of deformable solids (74-XX) 5 Ordinary differential equations (34-XX) 5 Calculus of variations and optimal control; optimization (49-XX) 4 Mechanics of particles and systems (70-XX) 4 Geophysics (86-XX) 4 Systems theory; control (93-XX) 3 Approximations and expansions (41-XX) 3 Harmonic analysis on Euclidean spaces (42-XX) 3 Functional analysis (46-XX) 2 Operator theory (47-XX) 2 Global analysis, analysis on manifolds (58-XX) 2 Classical thermodynamics, heat transfer (80-XX) 2 Astronomy and astrophysics (85-XX) 1 Real functions (26-XX) 1 Dynamical systems and ergodic theory (37-XX) 1 Integral equations (45-XX) 1 Statistics (62-XX) 1 Optics, electromagnetic theory (78-XX) 1 Quantum theory (81-XX) 1 Relativity and gravitational theory (83-XX) 1 Game theory, economics, finance, and other social and behavioral sciences (91-XX) Citations by Year