Ghoshal, Shyam Sundar; Jana, Animesh; Towers, John D. Convergence of a Godunov scheme to an Audusse-Perthame adapted entropy solution for conservation laws with BV spatial flux. (English) Zbl 1451.65107 Numer. Math. 146, No. 3, 629-659 (2020). MSC: 65M06 65M12 35L65 35B44 35A01 65M08 76M20 PDF BibTeX XML Cite \textit{S. S. Ghoshal} et al., Numer. Math. 146, No. 3, 629--659 (2020; Zbl 1451.65107) Full Text: DOI
Towers, John D. An existence result for conservation laws having BV spatial flux heterogeneities – without concavity. (English) Zbl 1440.35213 J. Differ. Equations 269, No. 7, 5754-5764 (2020). MSC: 35L65 35L03 35L60 35B44 35A01 65M06 PDF BibTeX XML Cite \textit{J. D. Towers}, J. Differ. Equations 269, No. 7, 5754--5764 (2020; Zbl 1440.35213) Full Text: DOI
Towers, John D. The Lax-Friedrichs scheme for interaction between the inviscid Burgers equation and multiple particles. (English) Zbl 1436.65112 Netw. Heterog. Media 15, No. 1, 143-169 (2020). MSC: 65M06 35F25 35L60 65M08 65M99 74F10 76M20 35D30 35Q35 PDF BibTeX XML Cite \textit{J. D. Towers}, Netw. Heterog. Media 15, No. 1, 143--169 (2020; Zbl 1436.65112) Full Text: DOI
Towers, John D. Convergence via OSLC of the Godunov scheme for a scalar conservation law with time and space flux discontinuities. (English) Zbl 1395.65042 Numer. Math. 139, No. 4, 939-969 (2018). MSC: 65M08 65M12 35L65 PDF BibTeX XML Cite \textit{J. D. Towers}, Numer. Math. 139, No. 4, 939--969 (2018; Zbl 1395.65042) Full Text: DOI
Towers, John D. Convergence of the Godunov scheme for a scalar conservation law with time and space discontinuities. (English) Zbl 1406.35190 J. Hyperbolic Differ. Equ. 15, No. 2, 175-190 (2018). MSC: 35L65 65M06 65M08 65M12 PDF BibTeX XML Cite \textit{J. D. Towers}, J. Hyperbolic Differ. Equ. 15, No. 2, 175--190 (2018; Zbl 1406.35190) Full Text: DOI
Towers, John D. A source term method for Poisson problems on irregular domains. (English) Zbl 1422.65327 J. Comput. Phys. 361, 424-441 (2018). MSC: 65N06 35J05 PDF BibTeX XML Cite \textit{J. D. Towers}, J. Comput. Phys. 361, 424--441 (2018; Zbl 1422.65327) Full Text: DOI
Karlsen, K. H.; Towers, J. D. Convergence of a Godunov scheme for conservation laws with a discontinuous flux lacking the crossing condition. (English) Zbl 1380.65158 J. Hyperbolic Differ. Equ. 14, No. 4, 671-701 (2017). MSC: 65M06 35L65 PDF BibTeX XML Cite \textit{K. H. Karlsen} and \textit{J. D. Towers}, J. Hyperbolic Differ. Equ. 14, No. 4, 671--701 (2017; Zbl 1380.65158) Full Text: DOI
Towers, John D. A fixed grid, shifted stencil scheme for inviscid fluid-particle interaction. (English) Zbl 06638248 Appl. Numer. Math. 110, 26-40 (2016). MSC: 65 PDF BibTeX XML Cite \textit{J. D. Towers}, Appl. Numer. Math. 110, 26--40 (2016; Zbl 06638248) Full Text: DOI
Bürger, Raimund; Karlsen, Kenneth H.; Towers, John D. On some difference schemes and entropy conditions for a class of multi-species kinematic flow models with discontinuous flux. (English) Zbl 1263.76048 Netw. Heterog. Media 5, No. 3, 461-485 (2010). MSC: 76M25 65M06 76T99 90B20 PDF BibTeX XML Cite \textit{R. Bürger} et al., Netw. Heterog. Media 5, No. 3, 461--485 (2010; Zbl 1263.76048) Full Text: DOI
Towers, John D. Finite difference methods for discretizing singular source terms in a Poisson interface problem. (English) Zbl 1216.65143 Holden, Helge (ed.) et al., Nonlinear partial differential equations and hyperbolic wave phenomena. The 2008–2009 research program on nonlinear partial differential equations, Centre for Advanced Study at the Norwegian Academy of Science and Letters, Oslo, Norway. Providence, RI: American Mathematical Society (AMS) (ISBN 978-0-8218-4976-7/pbk). Contemporary Mathematics 526, 359-389 (2010). MSC: 65N06 65N12 65N15 35J05 35R05 PDF BibTeX XML Cite \textit{J. D. Towers}, Contemp. Math. 526, 359--389 (2010; Zbl 1216.65143)
Bürger, Raimund; Karlsen, Kenneth H.; Torres, Héctor; Towers, John D. Second-order schemes for conservation laws with discontinuous flux modelling clarifier-thickener units. (English) Zbl 1204.65101 Numer. Math. 116, No. 4, 579-617 (2010). Reviewer: Gisbert Stoyan (Budapest) MSC: 65M06 65M12 PDF BibTeX XML Cite \textit{R. Bürger} et al., Numer. Math. 116, No. 4, 579--617 (2010; Zbl 1204.65101) Full Text: DOI
Bürger, Raimund; Karlsen, Kenneth H.; Towers, John D. An Engquist-Osher-type scheme for conservation laws with discontinuous flux adapted to flux connections. (English) Zbl 1201.35022 SIAM J. Numer. Anal. 47, No. 3, 1684-1712 (2009). Reviewer: Qin Mengzhao (Beijing) MSC: 35A35 35L65 65M06 35L45 PDF BibTeX XML Cite \textit{R. Bürger} et al., SIAM J. Numer. Anal. 47, No. 3, 1684--1712 (2009; Zbl 1201.35022) Full Text: DOI
Bürger, Raimund; Karlsen, Kenneth H.; Towers, John D. A conservation law with discontinuous flux modelling traffic flow with abruptly changing road surface conditions. (English) Zbl 1186.35005 Tadmor, Eitan (ed.) et al., Hyperbolic problems. Theory, numerics and applications. Contributed talks. Proceedings of the 12th international conference on hyperbolic problems, June 9–13, 2008. Providence, RI: American Mathematical Society (AMS) (ISBN 978-0-8218-4730-5/hbk; 978-0-8218-4728-2/2-vol. set). Proceedings of Symposia in Applied Mathematics 67, Part 2, 455-464 (2009). Reviewer: Prabhat Kumar Mahanti (Saint John) MSC: 35A35 65M06 35L65 90B20 PDF BibTeX XML Cite \textit{R. Bürger} et al., Proc. Symp. Appl. Math. 67, 455--464 (2009; Zbl 1186.35005)
Towers, John D. Discretizing delta functions via finite differences and gradient normalization. (English) Zbl 1167.65007 J. Comput. Phys. 228, No. 10, 3816-3836 (2009). Reviewer: Martin D. Buhmann (Gießen) MSC: 65D15 46F10 PDF BibTeX XML Cite \textit{J. D. Towers}, J. Comput. Phys. 228, No. 10, 3816--3836 (2009; Zbl 1167.65007) Full Text: DOI
Towers, John D. Finite difference methods for approximating Heaviside functions. (English) Zbl 1171.65014 J. Comput. Phys. 228, No. 9, 3478-3489 (2009). Reviewer: Jesus Illán González (Vigo) MSC: 65D32 41A55 41A25 41A63 PDF BibTeX XML Cite \textit{J. D. Towers}, J. Comput. Phys. 228, No. 9, 3478--3489 (2008; Zbl 1171.65014) Full Text: DOI
Bürger, Raimund; García, Antonio; Karlsen, Kenneth H.; Towers, John D. Difference schemes, entropy solutions, and speedup impulse for an inhomogeneous kinematic traffic flow model. (English) Zbl 1173.35586 Netw. Heterog. Media 3, No. 1, 1-41 (2008). Reviewer: Argiris I. Delis (Chania) MSC: 35L65 65M06 90B20 35L45 PDF BibTeX XML Cite \textit{R. Bürger} et al., Netw. Heterog. Media 3, No. 1, 1--41 (2008; Zbl 1173.35586) Full Text: DOI Link
Towers, John D. A convergence rate theorem for finite difference approximations to delta functions. (English) Zbl 1155.65016 J. Comput. Phys. 227, No. 13, 6591-6597 (2008). Reviewer: Vasilis Dimitriou (Chania) MSC: 65D15 PDF BibTeX XML Cite \textit{J. D. Towers}, J. Comput. Phys. 227, No. 13, 6591--6597 (2008; Zbl 1155.65016) Full Text: DOI
Towers, John D. Two methods for discretizing a delta function supported on a level set. (English) Zbl 1115.65028 J. Comput. Phys. 220, No. 2, 915-931 (2007). Reviewer: Manfred Tasche (Rostock) MSC: 65D32 58C35 46F10 41A55 PDF BibTeX XML Cite \textit{J. D. Towers}, J. Comput. Phys. 220, No. 2, 915--931 (2007; Zbl 1115.65028) Full Text: DOI
Bürger, R.; Garcia, A.; Karlsen, K. H.; Towers, J. D. On an extended clarifier-thickener model with singular source and sink terms. (English) Zbl 1201.35130 Eur. J. Appl. Math. 17, No. 3, 257-292 (2006). MSC: 35L60 76M20 76T20 65M06 PDF BibTeX XML Cite \textit{R. Bürger} et al., Eur. J. Appl. Math. 17, No. 3, 257--292 (2006; Zbl 1201.35130) Full Text: DOI
Bürger, Raimund; Karlsen, Kenneth H.; Towers, John D. Closed-form and finite difference solutions to a population balance model of grinding mills. (English) Zbl 1097.74045 J. Eng. Math. 51, No. 2, 165-195 (2005). MSC: 74M15 74H05 74S20 80M20 65M06 82C70 92D25 PDF BibTeX XML Cite \textit{R. Bürger} et al., J. Eng. Math. 51, No. 2, 165--195 (2005; Zbl 1097.74045) Full Text: DOI
Bürger, Raimund; Karlsen, Kenneth H.; Towers, John D. A model of continuous sedimentation of flocculated suspensions in clarifier-thickener units. (English) Zbl 1089.76061 SIAM J. Appl. Math. 65, No. 3, 882-940 (2005). MSC: 76T20 76M20 65M12 35Q35 PDF BibTeX XML Cite \textit{R. Bürger} et al., SIAM J. Appl. Math. 65, No. 3, 882--940 (2005; Zbl 1089.76061) Full Text: DOI
Karlsen, K. H.; Towers, J. D. Convergence of the Lax-Friedrichs scheme and stability for conservation laws with a discontinuous space-time dependent flux. (English) Zbl 1112.65085 Chin. Ann. Math., Ser. B 25, No. 3, 287-318 (2004). Reviewer: Andreas Meister (Kassel) MSC: 65M12 35L65 PDF BibTeX XML Cite \textit{K. H. Karlsen} and \textit{J. D. Towers}, Chin. Ann. Math., Ser. B 25, No. 3, 287--318 (2004; Zbl 1112.65085) Full Text: DOI
Bürger, R.; Karlsen, K. H.; Risebro, N. H.; Towers, J. D. Well-posedness in \(BV_t\) and convergence of a difference scheme for continuous sedimentation in ideal clarifier-thickener units. (English) Zbl 1053.76047 Numer. Math. 97, No. 1, 25-65 (2004). MSC: 76M20 76T20 65M12 65M06 35L65 35R05 PDF BibTeX XML Cite \textit{R. Bürger} et al., Numer. Math. 97, No. 1, 25--65 (2004; Zbl 1053.76047) Full Text: DOI
Karlsen, K. H.; Risebro, N. H.; Towers, J. D. Upwind difference approximations for degenerate parabolic convection-diffusion equations with a discontinuous coefficient. (English) Zbl 1014.65073 IMA J. Numer. Anal. 22, No. 4, 623-664 (2002). Reviewer: Xavier Antoine (Toulouse Cedex) MSC: 65M06 65M12 35K65 35R05 PDF BibTeX XML Cite \textit{K. H. Karlsen} et al., IMA J. Numer. Anal. 22, No. 4, 623--664 (2002; Zbl 1014.65073) Full Text: DOI
Towers, John D. A difference scheme for conservation laws with a discontinuous flux: the nonconvex case. (English) Zbl 1055.65104 SIAM J. Numer. Anal. 39, No. 4, 1197-1218 (2001). Reviewer: Oscar Lopez-Pouso (Santiago de Compostela) MSC: 65M06 35L65 65M12 35A35 PDF BibTeX XML Cite \textit{J. D. Towers}, SIAM J. Numer. Anal. 39, No. 4, 1197--1218 (2001; Zbl 1055.65104) Full Text: DOI
Towers, John D. Convergence of a difference scheme for conservation laws with a discontinuous flux. (English) Zbl 0972.65060 SIAM J. Numer. Anal. 38, No. 2, 681-698 (2000). Reviewer: Michael Sever (Jerusalem) MSC: 65M12 65M06 35L65 35R05 PDF BibTeX XML Cite \textit{J. D. Towers}, SIAM J. Numer. Anal. 38, No. 2, 681--698 (2000; Zbl 0972.65060) Full Text: DOI