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. 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.; 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)
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
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, R.; García, A.; Karlsen, K. H.; Towers, J. D. A note on an extended clarifier-thickener model with singular source and sink terms. (English) Zbl 1115.35351 Sci., Ser. A, Math. Sci. (N.S.) 13, 36-44 (2006). MSC: 35L65 76T20 35R05 PDF BibTeX XML Cite \textit{R. Bürger} et al., Sci., Ser. A, Math. Sci. (N.S.) 13, 36--44 (2006; Zbl 1115.35351)
Bürger, Raimund; Karlsen, Kenneth H.; Towers, John D. A mathematical model of clarifier-thickener units. (English) Zbl 1391.76789 PAMM, Proc. Appl. Math. Mech. 5, 589-590 (2005). MSC: 76T20 35Q35 76M25 PDF BibTeX XML Cite \textit{R. Bürger} et al., PAMM, Proc. Appl. Math. Mech. 5, 589--590 (2005; Zbl 1391.76789) 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
Bürger, Raimund; Karlsen, Kenneth H.; Mishra, Siddharta; Towers, John D. On conservation laws with discontinuous flux. (English) Zbl 1076.76069 Wang, Yongqi (ed.) et al., Trends in applications of mathematics to mechanics. Proceedings of the international symposium, STAMM, Seeheim, Germany, August 22–28, 2004. Aachen: Shaker (ISBN 3-8322-3600-7/pbk). Berichte aus der Mathematik, 75-84 (2005). Reviewer: Boris V. Loginov (Ul’yanovsk) MSC: 76S05 76T30 74S30 35L65 PDF BibTeX XML Cite \textit{R. Bürger} et al., in: Trends in applications of mathematics to mechanics. Proceedings of the international symposium, STAMM, Seeheim, Germany, August 22--28, 2004. Aachen: Shaker Verlag. 75--84 (2005; Zbl 1076.76069)
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
Karlsen, K. H.; Risebro, N. H.; Towers, J. D. Front tracking for scalar balance equations. (English) Zbl 1053.35088 J. Hyperbolic Differ. Equ. 1, No. 1, 115-148 (2004). Reviewer: Mária Lukáčová (Hamburg) MSC: 35L60 35L45 76M25 35L65 35A35 PDF BibTeX XML Cite \textit{K. H. Karlsen} et al., J. Hyperbolic Differ. Equ. 1, No. 1, 115--148 (2004; Zbl 1053.35088) 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. \(L^1\) stability for entropy solutions of nonlinear degenerate parabolic convection-diffusion equations with discontinuous coefficients. (English) Zbl 1036.35104 Skr., K. Nor. Vidensk. Selsk. 2003, No. 3, 49 p. (2003). Reviewer: Angela Handlovičová (Bratislava) MSC: 35K65 35K57 35B35 35R05 PDF BibTeX XML Cite \textit{K. H. Karlsen} et al., Skr., K. Nor. Vidensk. Selsk. 2003, No. 3, 49 p. (2003; Zbl 1036.35104)
Karlsen, Kenneth H.; Risebro, Nils H.; Towers, John D. On a nonlinear degenerate parabolic transport-diffusion equation with a discontinuous coefficient. (English) Zbl 1015.35049 Electron. J. Differ. Equ. 2002, Paper No. 93, 23 p. (2002). Reviewer: Giovanni Porru (Cagliari) MSC: 35K65 35R05 35L80 35D05 PDF BibTeX XML Cite \textit{K. H. Karlsen} et al., Electron. J. Differ. Equ. 2002, Paper No. 93, 23 p. (2002; Zbl 1015.35049) Full Text: EMIS EuDML
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