## Towers, John D.

Compute Distance To:
 Author ID: towers.john-d Published as: Towers, John D.; Towers, J. D.
 Documents Indexed: 40 Publications since 2000 Co-Authors: 8 Co-Authors with 25 Joint Publications 216 Co-Co-Authors
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### Co-Authors

 15 single-authored 22 Karlsen, Kenneth Hvistendahl 15 Bürger, Raimund 7 Risebro, Nils Henrik 3 Ghoshal, Shyam Sundar 2 Vaidya, Ganesh 1 Jana, Animesh 1 Mishra, Siddhartha 1 Torres, Héctor
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### 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 Scientia. Series A: Mathematical Sciences. New Series 1 PAMM. Proceedings in Applied Mathematics and Mechanics 1 Advances in Applied Mathematics and Mechanics
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### Fields

 30 Numerical analysis (65-XX) 29 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)

### Citations contained in zbMATH Open

33 Publications have been cited 671 times in 238 Documents Cited by Year
Convergence of a difference scheme for conservation laws with a discontinuous flux. Zbl 0972.65060
Towers, John D.
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.
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.
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.
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.
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.
2009
A difference scheme for conservation laws with a discontinuous flux: the nonconvex case. Zbl 1055.65104
Towers, John D.
2001
A family of numerical schemes for kinematic flows with discontinuous flux. Zbl 1200.76126
Bürger, R.; García, A.; Karlsen, K. H.; Towers, J. D.
2008
A model of continuous sedimentation of flocculated suspensions in clarifier-thickener units. Zbl 1089.76061
Bürger, Raimund; Karlsen, Kenneth H.; Towers, John D.
2005
Two methods for discretizing a delta function supported on a level set. Zbl 1115.65028
Towers, John D.
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.
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.
2004
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.
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.
2010
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.
2017
Finite difference methods for approximating Heaviside functions. Zbl 1171.65014
Towers, John D.
2008
Front tracking for scalar balance equations. Zbl 1053.35088
Karlsen, K. H.; Risebro, N. H.; Towers, J. D.
2004
A convergence rate theorem for finite difference approximations to delta functions. Zbl 1155.65016
Towers, John D.
2008
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.
2006
An existence result for conservation laws having BV spatial flux heterogeneities – without concavity. Zbl 1440.35213
Towers, John D.
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.
2009
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.
2003
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.
2010
A source term method for Poisson problems on irregular domains. Zbl 1422.65327
Towers, John D.
2018
Convergence of the Godunov scheme for a scalar conservation law with time and space discontinuities. Zbl 1406.35190
Towers, John D.
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.
2018
On conservation laws with discontinuous flux. Zbl 1076.76069
Bürger, Raimund; Karlsen, Kenneth H.; Mishra, Siddharta; Towers, John D.
2005
Discretizing delta functions via finite differences and gradient normalization. Zbl 1167.65007
Towers, John D.
2009
Finite difference methods for discretizing singular source terms in a Poisson interface problem. Zbl 1216.65143
Towers, John D.
2010
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.
2020
A fixed grid, shifted stencil scheme for inviscid fluid-particle interaction. Zbl 06638248
Towers, John D.
2016
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.
2005
Convergence of monotone schemes for conservation laws with zero-flux boundary conditions. Zbl 1488.65365
Karlsen, K. H.; Towers, J. D.
2017
An existence result for conservation laws having BV spatial flux heterogeneities – without concavity. Zbl 1440.35213
Towers, John D.
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.
2020
A source term method for Poisson problems on irregular domains. Zbl 1422.65327
Towers, John D.
2018
Convergence of the Godunov scheme for a scalar conservation law with time and space discontinuities. Zbl 1406.35190
Towers, John D.
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.
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.
2017
Convergence of monotone schemes for conservation laws with zero-flux boundary conditions. Zbl 1488.65365
Karlsen, K. H.; Towers, J. D.
2017
A fixed grid, shifted stencil scheme for inviscid fluid-particle interaction. Zbl 06638248
Towers, John D.
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.
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.
2010
Finite difference methods for discretizing singular source terms in a Poisson interface problem. Zbl 1216.65143
Towers, John D.
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.
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.
2009
Discretizing delta functions via finite differences and gradient normalization. Zbl 1167.65007
Towers, John D.
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.
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.
2008
Finite difference methods for approximating Heaviside functions. Zbl 1171.65014
Towers, John D.
2008
A convergence rate theorem for finite difference approximations to delta functions. Zbl 1155.65016
Towers, John D.
2008
Two methods for discretizing a delta function supported on a level set. Zbl 1115.65028
Towers, John D.
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.
2006
A model of continuous sedimentation of flocculated suspensions in clarifier-thickener units. Zbl 1089.76061
Bürger, Raimund; Karlsen, Kenneth H.; Towers, John D.
2005
On conservation laws with discontinuous flux. Zbl 1076.76069
Bürger, Raimund; Karlsen, Kenneth H.; Mishra, Siddharta; Towers, John D.
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.
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.
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.
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.
2004
Front tracking for scalar balance equations. Zbl 1053.35088
Karlsen, K. H.; Risebro, N. H.; Towers, J. D.
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.
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.
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.
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.
2002
A difference scheme for conservation laws with a discontinuous flux: the nonconvex case. Zbl 1055.65104
Towers, John D.
2001
Convergence of a difference scheme for conservation laws with a discontinuous flux. Zbl 0972.65060
Towers, John D.
2000
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### Cited by 293 Authors

 27 Bürger, Raimund 21 Karlsen, Kenneth Hvistendahl 17 Risebro, Nils Henrik 17 Towers, John D. 14 Andreianov, Boris 11 Diehl, Stefan 11 Mishra, Siddhartha 9 Gowda, G. D. Veerappa 8 Adimurthi, A. 7 Goatin, Paola 6 Cancès, Clément 6 Ghoshal, Shyam Sundar 5 Coclite, Giuseppe Maria 5 Gibou, Frédéric 5 Klingenberg, Christian 5 Panov, Evgeniy Yu. 5 Wang, Guodong 5 Wong, Sze Chun 4 Abreu, Eduardo 4 Lu, Yunguang 4 Sepúlveda, Mauricio A. 4 Shen, Chun 4 Sylla, Abraham 4 Villada, Luis Miguel 3 Berres, Stefan 3 Chalons, Christophe 3 Choi, Keechoo 3 Guerra, Graziano 3 Koley, Ujjwal 3 Kublik, Catherine M. 3 Qiao, Dianliang 3 Rosini, Massimiliano Daniele 3 Rossi, Elena 3 Seaïd, Mohammed 3 Shen, Wen 3 Sun, Meina 3 Tsai, Yen-Hsi Richard 3 Wen, Xin 2 Acosta, Carlos Daniel 2 Amadori, Debora 2 Aniszewski, Wojciech 2 Badwaik, Jayesh 2 Briani, Maya 2 Bustos, Abel 2 Coronel, Aníbal 2 Cristiani, Emiliano 2 Donadello, Carlotta 2 Dutta, Rajib 2 Egan, Raphael 2 Eymard, Robert 2 Farås, Sebastian 2 Festa, Adriano 2 Fjordholm, Ulrik Skre 2 Gosse, Laurent 2 Göttlich, Simone 2 Gwiazda, Piotr 2 Hilhorst, Danielle 2 Kolahdouz, Ebrahim M. 2 Kröker, Ilja 2 Krunić, Tanja 2 Kumar Kenettinkara, Sudarshan 2 Kummer, Florian 2 Lambert, Wanderson J. 2 Lin, Zhiyang 2 Liu, Jianguo 2 Ma, Yanying 2 Mejía, Carlos E. 2 Min, Chohong 2 Mitrovic, Darko 2 Müller, Björn 2 Musch, Markus 2 Nedeljkov, Marko 2 Oberlack, Martin 2 Piccoli, Benedetto 2 Ruf, Adrian M. 2 Ruiz, Ricardo M. 2 Saad, Mazen 2 Salac, David 2 Saye, Robert I. 2 Schneider, Kai 2 Seguin, Nicolas 2 Shu, Chi-Wang 2 Sudarshan Kumar, Kenettinkara 2 Świerczewska-Gwiazda, Agnieszka 2 Tang, Min 2 Tsokaros, Antonios A. 2 Vaidya, Ganesh 2 Vohralík, Martin 2 Vovelle, Julien 2 Wang, Li 2 Wang, Zhongming 2 Wolgemuth, Charles W. 2 Zhang, Tiankui 2 Zhou, Zhennan 1 Aggarwal, Aekta 1 Ammar, Kaouther 1 Ancona, Fabio 1 Auguste, Franck 1 Bachmann, Florence 1 Bäcker, Jan-Phillip ...and 193 more Authors
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### Cited in 73 Serials

 30 Journal of Computational Physics 12 Journal of Differential Equations 12 Networks and Heterogeneous Media 11 Journal of Hyperbolic Differential Equations 10 European Series in Applied and Industrial Mathematics (ESAIM): Mathematical Modelling and Numerical Analysis 9 Journal of Engineering Mathematics 8 Mathematics of Computation 8 Numerische Mathematik 7 M$$^3$$AS. Mathematical Models & Methods in Applied Sciences 6 Applied Numerical Mathematics 6 Journal of Scientific Computing 5 Computers & Mathematics with Applications 5 Applied Mathematics and Computation 5 Journal of Computational and Applied Mathematics 5 Applied Mathematical Modelling 4 Archive for Rational Mechanics and Analysis 4 ZAMP. Zeitschrift für angewandte Mathematik und Physik 4 SIAM Journal on Numerical Analysis 4 Applied Mathematics Letters 4 SIAM Journal on Applied Mathematics 4 SIAM Journal on Mathematical Analysis 4 Computational Geosciences 3 Journal of Mathematical Analysis and Applications 3 International Journal for Numerical Methods in Engineering 3 Numerical Methods for Partial Differential Equations 3 SIAM Journal on Scientific Computing 2 Computer Methods in Applied Mechanics and Engineering 2 Journal of Functional Analysis 2 Acta Applicandae Mathematicae 2 Journal of Mathematical Sciences (New York) 2 ZAMM. Zeitschrift für Angewandte Mathematik und Mechanik 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 Applicable Analysis 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 Physica A 1 Annales Universitatis Mariae Curie-Skłodowska. Sectio A. Mathematica 1 BIT 1 Calcolo 1 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods 1 Transactions of the American Mathematical Society 1 Applied Mathematics and Mechanics. (English Edition) 1 Annales de l’Institut Henri Poincaré. Analyse Non Linéaire 1 Mathematical and Computer Modelling 1 Communications in Partial Differential Equations 1 Communications in Numerical Methods in Engineering 1 Computational and Applied Mathematics 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 M2AN. Mathematical Modelling and Numerical Analysis. ESAIM, European Series in Applied and Industrial Mathematics 1 Nonlinear Analysis. Real World Applications 1 Journal of Evolution Equations 1 Central European Journal of Mathematics 1 Multiscale Modeling & Simulation 1 Granular Matter 1 International Journal of Computational Methods 1 International Journal of Numerical Analysis and Modeling 1 Mathematical Biosciences and Engineering 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 Research in the Mathematical Sciences 1 Journal of Elliptic and Parabolic Equations 1 International Journal on Finite Volumes
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### Cited in 25 Fields

 168 Partial differential equations (35-XX) 142 Numerical analysis (65-XX) 86 Fluid mechanics (76-XX) 30 Operations research, mathematical programming (90-XX) 8 Statistical mechanics, structure of matter (82-XX) 8 Biology and other natural sciences (92-XX) 6 Probability theory and stochastic processes (60-XX) 5 Calculus of variations and optimal control; optimization (49-XX) 5 Mechanics of deformable solids (74-XX) 4 Mechanics of particles and systems (70-XX) 3 Approximations and expansions (41-XX) 3 Functional analysis (46-XX) 3 Geophysics (86-XX) 2 Ordinary differential equations (34-XX) 2 Operator theory (47-XX) 2 Classical thermodynamics, heat transfer (80-XX) 2 Astronomy and astrophysics (85-XX) 2 Systems theory; control (93-XX) 1 Dynamical systems and ergodic theory (37-XX) 1 Harmonic analysis on Euclidean spaces (42-XX) 1 Global analysis, analysis on manifolds (58-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)