Edit Profile Risebro, Nils Henrik Compute Distance To: Compute Author ID: risebro.nils-henrik Published as: Risebro, Nils Henrik; Risebro, N. H.; Risebro, Nils H. Documents Indexed: 118 Publications since 1990, including 5 Books all top 5 Co-Authors 3 single-authored 46 Karlsen, Kenneth Hvistendahl 36 Holden, Helge 17 Mishra, Siddhartha 15 Coclite, Giuseppe Maria 9 Koley, Ujjwal 7 Towers, John D. 6 Klingenberg, Christian 6 Lie, Knut-Andreas 5 Fuchs, Franz Georg 5 Storrøsten, Erlend Briseid 5 Weber, Franziska 4 Dutta, Rajib 4 Gimse, Tore 4 Sande, Hilde 4 Schwab, Christoph 4 Tveito, Aslak 3 McMurry, Andrew D. 3 Waagan, Knut 2 Andreianov, Boris 2 Hanche-Olsen, Harald 2 Hoel, Hakon A. 2 Holden, Lars 2 Jakobsen, Espen Robstad 2 Klausen, Runhild Aae 2 Ridder, Johanna 2 Ruf, Adrian M. 2 Svärd, Magnus 1 Agrell, Christian 1 Badwaik, Jayesh 1 Bratvedt, Frode 1 Bratvedt, Kyrre 1 Buchholz, Christian F. 1 Bürger, Raimund 1 Colombo, Rinaldo M. 1 Evje, Steinar 1 Frid, Hermano 1 Gesztesy, Fritz 1 Hvistendahl, K. 1 Langseth, Jan Olav 1 Larssen, Bjørnar 1 Lubich, Christian 1 Lyubarskii, Yurii I. 1 Martinsen, Torgeir With 1 Priuli, Fabio Simone 1 Reichmann, Oleg 1 Seip, Kristian 1 Tao, Terence 1 Tokareva, Svetlana A. all top 5 Serials 8 Mathematics of Computation 6 Journal of Computational Physics 5 IMA Journal of Numerical Analysis 5 BIT 5 Numerische Mathematik 5 SIAM Journal on Numerical Analysis 5 SIAM Journal on Mathematical Analysis 5 Journal of Hyperbolic Differential Equations 4 Journal of Differential Equations 3 ZAMP. Zeitschrift für angewandte Mathematik und Physik 3 International Journal of Numerical Analysis and Modeling 3 European Series in Applied and Industrial Mathematics (ESAIM): Mathematical Modelling and Numerical Analysis 3 Applied Mathematical Sciences 2 Journal of Engineering Mathematics 2 Communications in Partial Differential Equations 2 SIAM Journal on Applied Mathematics 2 Electronic Journal of Differential Equations (EJDE) 2 Discrete and Continuous Dynamical Systems 2 Computational Geosciences 2 Communications in Computational Physics 2 Networks and Heterogeneous Media 1 Archive for Rational Mechanics and Analysis 1 Computers & Mathematics with Applications 1 Inverse Problems 1 Journal of Mathematical Analysis and Applications 1 Nonlinearity 1 Zeitschrift für Angewandte Mathematik und Mechanik (ZAMM) 1 Applied Mathematics and Optimization 1 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods 1 Proceedings of the American Mathematical Society 1 Quarterly of Applied Mathematics 1 SIAM Journal on Scientific and Statistical Computing 1 Stochastic Analysis and Applications 1 Applied Numerical Mathematics 1 Surveys on Mathematics for Industry 1 Advances in Differential Equations 1 Skrifter. Det Kongelige Norske Videnskabers Selskab 1 Computing and Visualization in Science 1 Vietnam Journal of Mathematics 1 M2AN. Mathematical Modelling and Numerical Analysis. ESAIM, European Series in Applied and Industrial Mathematics 1 Nonlinear Analysis. Real World Applications 1 Milan Journal of Mathematics 1 Bollettino dell’Unione Matematica Italiana. Series IX 1 S\(\vec{\text{e}}\)MA Journal 1 Stochastic and Partial Differential Equations. Analysis and Computations 1 SIAM/ASA Journal on Uncertainty Quantification 1 EMS Series of Lectures in Mathematics 1 EMS Series of Congress Reports all top 5 Fields 104 Partial differential equations (35-XX) 64 Numerical analysis (65-XX) 42 Fluid mechanics (76-XX) 8 Probability theory and stochastic processes (60-XX) 7 Statistical mechanics, structure of matter (82-XX) 5 Operations research, mathematical programming (90-XX) 4 Mechanics of deformable solids (74-XX) 3 Optics, electromagnetic theory (78-XX) 3 Geophysics (86-XX) 2 Operator theory (47-XX) 2 Calculus of variations and optimal control; optimization (49-XX) 2 Mechanics of particles and systems (70-XX) 1 General and overarching topics; collections (00-XX) 1 Ordinary differential equations (34-XX) 1 Integral equations (45-XX) 1 Functional analysis (46-XX) 1 Astronomy and astrophysics (85-XX) 1 Systems theory; control (93-XX) Publications by Year all cited Publications top 5 cited Publications Citations contained in zbMATH Open 105 Publications have been cited 1,713 times in 890 Documents Cited by ▼ Year ▼ Front tracking for hyperbolic conservation laws. Zbl 1006.35002Holden, Helge; Risebro, Nils Henrik 89 2002 Solution of the Cauchy problem for a conservation law with a discontinuous flux function. Zbl 0776.35034Gimse, Tore; Risebro, Nils Henrik 74 1992 A mathematical model of traffic flow on a network of unidirectional roads. Zbl 0833.35089Holden, Helge; Risebro, Nils Henrik 70 1995 A theory of \(L ^{1}\)-dissipative solvers for scalar conservation laws with discontinuous flux. Zbl 1261.35088Andreianov, Boris; Karlsen, Kenneth Hvistendahl; Risebro, Nils Henrik 68 2011 \(L^1\) stability for entropy solutions of nonlinear degenerate parabolic convection-diffusion equations with discontinuous coefficients. Zbl 1036.35104Karlsen, K. H.; Risebro, N. H.; Towers, J. D. 65 2003 Convex conservation laws with discontinuous coefficients. Existence, uniqueness and asymptotic behavior. Zbl 0836.35090Klingenberg, Christian; Risebro, Nils Henrik 62 1995 On the uniqueness and stability of entropy solutions of nonlinear degenerate parabolic equations with rough coefficients. Zbl 1027.35057Karlsen, Kenneth Hvistendahl; Risebro, Nils Henrik 62 2003 Splitting methods for partial differential equations with rough solutions. Analysis and Matlab programs. Zbl 1191.35005Holden, Helge; Karlsen, Kenneth H.; Lie, Knut-Andreas; Risebro, Nils Henrik 53 2010 Upwind difference approximations for degenerate parabolic convection-diffusion equations with a discontinuous coefficient. Zbl 1014.65073Karlsen, K. H.; Risebro, N. H.; Towers, J. D. 53 2002 Well-posedness in \(BV_t\) and convergence of a difference scheme for continuous sedimentation in ideal clarifier-thickener units. Zbl 1053.76047Bürger, R.; Karlsen, K. H.; Risebro, N. H.; Towers, J. D. 52 2004 Front tracking for hyperbolic conservation laws. 2nd edition. Zbl 1346.35004Holden, Helge; Risebro, Nils Henrik 52 2015 Riemann problems with a discontinuous flux function. Zbl 0789.35102Gimse, Tore; Risebro, Nils Henrik 40 1991 Stability of conservation laws with discontinuous coefficients. Zbl 0935.35097Klausen, Runhild Aae; Risebro, Nils Henrik 32 1999 Convergence of finite difference schemes for viscous and inviscid conservation laws with rough coefficients. Zbl 1032.76048Karlsen, Kenneth Hvistendahl; Risebro, Nils Henrik 32 2001 Operator splitting for the KdV equation. Zbl 1219.35235Holden, Helge; Karlsen, Kenneth H.; Risebro, Nils Henrik; Tao, Terence 29 2011 Conservation laws with a random source. Zbl 0885.35069Holden, H.; Risebro, N. H. 29 1997 Operator splitting for partial differential equations with Burgers nonlinearity. Zbl 1260.35184Holden, Helge; Lubich, Christian; Risebro, Nils Henrik 28 2013 Numerical schemes for computing discontinuous solutions of the Degasperis-Procesi equation. Zbl 1246.76114Coclite, G. M.; Karlsen, K. H.; Risebro, N. H. 28 2008 On vanishing viscosity approximation of conservation laws with discontinuous flux. Zbl 1270.35305Andreianov, Boris; Karlsen, Kenneth H.; Risebro, Nils H. 27 2010 Stability of a resonant system of conservation laws modeling polymer flow with gravitation. Zbl 0977.35083Klingenberg, Christian; Risebro, Nils Henrik 27 2001 A front-tracking alternative to the random choice method. Zbl 0799.35153Risebro, Nils Henrik 26 1993 A front tracking approach to a model of continuous sedimentation in ideal clarifier-thickener units. Zbl 1013.35052Bürger, R.; Karlsen, K. H.; Klingenberg, C.; Risebro, N. H. 25 2003 Operator splitting methods for generalized Korteweg-de Vries equations. Zbl 0947.65102Holden, Helge; Karlsen, Kenneth Hvistendahl; Risebro, Nils Henrik 23 1999 When are HJB-equations in stochastic control of delay systems finite dimensional? Zbl 1052.60051Larssen, Bjørnar; Risebro, Nils Henrik 23 2003 Front tracking for hyperbolic conservation laws. Paperback ed. Zbl 1239.35003Holden, Helge; Risebro, Nils Henrik 22 2011 Conservation laws with time dependent discontinuous coefficients. Zbl 1078.35071Coclite, Giuseppe Maria; Risebro, Nils Henrik 22 2005 An operator splitting method for nonlinear convection-diffusion equations. Zbl 0882.35074Karlsen, Kenneth Hvistendahl; Risebro, Nils Henrik 21 1997 A convergent finite difference scheme for the Camassa–Holm equation with general \(H^1\) initial data. Zbl 1172.35310Coclite, G. M.; Karlsen, K. H.; Risebro, N. H. 20 2008 On a nonlinear degenerate parabolic transport-diffusion equation with a discontinuous coefficient. Zbl 1015.35049Karlsen, Kenneth H.; Risebro, Nils H.; Towers, John D. 17 2002 Front tracking applied to a nonstrictly hyperbolic system of conservation laws. Zbl 0736.65075Risebro, Nils Henrik; Tveito, Aslak 16 1991 Numerical solution of scalar conservation laws with random flux functions. Zbl 1343.65007Mishra, Siddhartha; Risebro, Nils Henrik; Schwab, Christoph; Tokareva, Svetlana 16 2016 Stable upwind schemes for the magnetic induction equation. Zbl 1177.78057Fuchs, Franz G.; Karlsen, Kenneth H.; Mishra, Siddharta; Risebro, Nils H. 15 2009 A front tracking method for conservation laws in one dimension. Zbl 0756.65120Risebro, N. H.; Tveito, A. 15 1992 Convergent difference schemes for the Hunter–Saxton equation. Zbl 1114.65101Holden, H.; Karlsen, K. H.; Risebro, N. H. 14 2007 Monotone difference approximations for the simulation of clarifier-thickener units. Zbl 1299.76283Bürger, R.; Karlsen, K. H.; Risebro, N. H.; Towers, J. D. 14 2004 On the convergence rate of operator splitting for Hamilton-Jacobi equations with source terms. Zbl 1059.70012Jakobsen, Espen Robstad; Karlsen, Kenneth Hvistendahl; Risebro, Nils Henrik 13 2001 A note on front tracking and the equivalence between viscosity solutions of Hamilton-Jacobi equations and entropy solutions of scalar conservation laws. Zbl 1010.35026Karlsen, Kenneth Hvistendahl; Risebro, Nils Henrik 13 2002 The continuum limit of follow-the-leader models – a short proof. Zbl 1378.35180Holden, Helge; Risebro, Nils Henrik 13 2018 Approximate Riemann solvers and robust high-order finite volume schemes for multi-dimensional ideal MHD equations. Zbl 1364.76113Fuchs, Franz Georg; McMurry, Andrew D.; Mishra, Siddhartha; Risebro, Nils Henrik; Waagan, Knut 13 2011 The solution of the Cauchy problem with large data for a model of a mixture of gases. Zbl 1178.35248Holden, Helge; Risebro, Nils Henrik; Sande, Hilde 12 2009 An unconditionally stable method for the Euler equations. Zbl 0922.76251Holden, Helge; Lie, Knut-Andreas; Risebro, Nils Henrik 12 1999 Corrected operator splitting for nonlinear parabolic equations. Zbl 0951.35080Karlsen, Kenneth Hvistendahl; Risebro, Nils Henrik 12 2000 A convergent finite difference scheme for the Ostrovsky-Hunter equation on a bounded domain. Zbl 1368.65133Coclite, G. M.; Ridder, J.; Risebro, N. H. 12 2017 An error estimate for the finite difference approximation to degenerate convection-diffusion equations. Zbl 1248.65098Karlsen, K. H.; Koley, U.; Risebro, N. H. 11 2012 Higher-order finite difference schemes for the magnetic induction equations with resistivity. Zbl 1252.78033Koley, U.; Mishra, S.; Risebro, N. H.; Svärd, M. 11 2012 Convergence of finite volume schemes for triangular systems of conservation laws. Zbl 1190.65133Karlsen, Kenneth Hvistendahl; Mishra, Siddhartha; Risebro, Nils Henrik 11 2009 Higher order finite difference schemes for the magnetic induction equations. Zbl 1168.78317Koley, Ujjwal; Mishra, Siddhartha; Risebro, Nils Henrik; Svärd, Magnus 11 2009 Continuous dependence in the large for some equations of gas dynamics. Zbl 0927.35082Colombo, Rinaldo M.; Risebro, Nils H. 11 1998 Convergence of a fully discrete finite difference scheme for the Korteweg-de Vries equation. Zbl 1348.65121Holden, Helge; Koley, Ujjwal; Risebro, Nils Henrik 11 2015 Splitting based finite volume schemes for ideal MHD equations. Zbl 1259.76021Fuchs, F. G.; Mishra, S.; Risebro, N. H. 10 2009 A relaxation scheme for continuous sedimentation in ideal clarifier-thickener units. Zbl 1122.76063Bürger, R.; Karlsen, K. H.; Risebro, N. H. 10 2005 A relaxation scheme for conservation laws with a discontinuous coefficient. Zbl 1078.65076Karlsen, K. H.; Klingenberg, C.; Risebro, N. H. 10 2004 A stochastic approach to conservation laws. Zbl 0789.35103Holden, H.; Risebro, N. H. 10 1991 Riemann problems with a kink. Zbl 0926.35087Holden, Helge; Risebro, Nils Henrik 10 1999 A method of fractional steps for scalar conservation laws without the CFL conditions. Zbl 0799.35150Holden, Helge; Risebro, Nils Henrik 10 1993 Convergence of an Engquist-Osher scheme for a multi-dimensional triangular system of conservation laws. Zbl 1369.65108Coclite, G. M.; Mishra, S.; Risebro, N. H. 9 2010 Viscosity solutions of Hamilton-Jacobi equations with discontinuous coefficients. Zbl 1144.35016Coclite, Giuseppe Maria; Risebro, Nils Henrik 9 2007 Unconditionally stable methods for Hamilton-Jacobi equations. Zbl 1143.65365Karlsen, Kenneth Hvistendahl; Risebro, Nils Henrik 9 2002 An explicit finite difference scheme for the Camassa-Holm equation. Zbl 1191.35021Coclite, Giuseppe Maria; Karlsen, Kenneth H.; Risebro, Nils Henrik 9 2008 \(L^{1}\) error estimates for difference approximations of degenerate convection-diffusion equations. Zbl 1300.65067Karlsen, K. H.; Risebro, N. H.; Storrøsten, E. B. 9 2014 High-order well-balanced finite volume schemes for simulating wave propagation in stratified magnetic atmospheres. Zbl 1190.76153Fuchs, F. G.; McMurry, A. D.; Mishra, S.; Risebro, N. H.; Waagan, K. 8 2010 A convergent finite-difference method for a nonlinear variational wave equation. Zbl 1236.65112Holden, H.; Karlsen, K. H.; Risebro, N. H. 8 2009 A fast marching method for reservoir simulation. Zbl 0997.76062Karlsen, K. Hvistendahl; Lie, K.-A.; Risebro, N. H. 8 2000 On uniqueness and existence of entropy solutions of weakly coupled systems of nonlinear degenerate parabolic equations. Zbl 1036.35102Holden, Helge; Karlsen, Kenneth H.; Risebro, Nils H. 8 2003 Follow-the-leader models can be viewed as a numerical approximation to the Lighthill-Whitham-Richards model for traffic flow. Zbl 1414.35122Holden, Helge; Risebro, Nils Henrik 8 2018 A multilevel Monte Carlo finite difference method for random scalar degenerate convection-diffusion equations. Zbl 1373.35179Koley, Ujjwal; Risebro, Nils Henrik; Schwab, Christoph; Weber, Franziska 8 2017 Front tracking for a model of immiscible gas flow with large data. Zbl 1425.76214Holden, Helge; Risebro, Nils Henrik; Sande, Hilde 7 2010 An introduction to the theory of scalar conservation laws with spatially discontinuous flux functions. Zbl 1191.74032Risebro, Nils Henrik 7 2009 FRONTLINE and FRONTSIM: Two full scale, two-phase, black oil reservoir simulators based on front tracking. Zbl 0780.76073Bratvedt, Frode; Bratvedt, Kyrre; Buchholz, Christian F.; Gimse, Tore; Holden, Helge; Holden, Lars; Risebro, Nils Henrik 7 1993 Convergence of a higher order scheme for the Korteweg-de Vries equation. Zbl 1342.35301Dutta, Rajib; Koley, Ujjwal; Risebro, Nils Henrik 7 2015 Well-balanced schemes for conservation laws with source terms based on a local discontinuous flux formulation. Zbl 1198.35149Karlsen, Kenneth Hvistendahl; Mishra, Siddhartha; Risebro, Nils Henrik 6 2009 Front tracking for scalar balance equations. Zbl 1053.35088Karlsen, K. H.; Risebro, N. H.; Towers, J. D. 6 2004 On a model for continuous sedimentation in vessels with discontinuous cross-sectional area. Zbl 1059.76542Bürger, R.; Karlsen, K. H.; Risebro, N. H.; Towers, J. D. 6 2003 Front tracking and operator splitting for nonlinear degenerate convection-diffusion equations. Zbl 0961.65073Evje, S.; Karlsen, K. Hvistendahl; Lie, K. A.; Risebro, N. H. 6 2000 Analysis and numerical approximation of Brinkman regularization of two-phase flows in porous media. Zbl 1392.76075Coclite, G. M.; Mishra, S.; Risebro, N. H.; Weber, F. 6 2014 Multilevel Monte Carlo front-tracking for random scalar conservation laws. Zbl 1350.65008Risebro, Nils Henrik; Schwab, Christoph; Weber, Franziska 6 2016 A hyperbolic-elliptic model of two-phase flow in porous media-existence of entropy solutions. Zbl 1277.76100Coclite, G. M.; Karlsen, K. H.; Mishra, S.; Risebro, N. H. 5 2012 Semi-Godunov schemes for multiphase flows in porous media. Zbl 1191.35022Karlsen, K. H.; Mishra, S.; Risebro, N. H. 5 2009 On the convergence rate of finite difference methods for degenerate convection-diffusion equations in several space dimensions. Zbl 1342.65182Karlsen, Kenneth Hvistendahl; Risebro, Nils Henrik; Storrøsten, Erlend Briseid 5 2016 A conservative front tracking scheme for 1D hyperbolic conservation laws. Zbl 0964.65517Langseth, Jan Olav; Risebro, Nils Henrik; Tveito, Aslak 4 1993 Path-dependent convex conservation laws. Zbl 1402.35170Hoel, H.; Karlsen, K. H.; Risebro, N. H.; Storrøsten, E. B. 4 2018 Convergence of vanishing viscosity approximations of \(2\times 2\) triangular systems of multi-dimensional conservation laws. Zbl 1178.35246Coclite, G. M.; Karlsen, K. H.; Mishra, S.; Risebro, N. H. 4 2009 Operator splitting for the Benjamin-Ono equation. Zbl 1326.35311Dutta, R.; Holden, H.; Koley, U.; Risebro, N. H. 4 2015 Models for dense multilane vehicular traffic. Zbl 1441.35162Holden, Helge; Risebro, Nils Henrik 4 2019 Some qualitative properties of 2\(\times 2\) systems of conservation laws of mixed type. Zbl 0718.76111Holden, H.; Holden, L.; Risebro, N. H. 3 1990 Stochastic properties of the scalar Buckley-Leverett equation. Zbl 0745.60064Holden, Helge; Risebro, Nils Henrik 3 1991 A front tracking method for conservation laws with boundary conditions. Zbl 0928.35098Hvistendahl, K.; Lie, K.-A.; Risebro, N. H. 3 1999 Convergence of finite difference schemes for the Benjamin-Ono equation. Zbl 1353.65090Dutta, Rajib; Holden, Helge; Koley, Ujjwal; Risebro, Nils Henrik 3 2016 On an inverse problem for scalar conservation laws. Zbl 1286.35266Holden, Helge; Priuli, Fabio Simone; Risebro, Nils Henrik 3 2014 A difference method for the McKean-Vlasov equation. Zbl 1423.35382Coclite, Giuseppe Maria; Risebro, Nils Henrik 3 2019 A convergent difference scheme for a class of partial integro-differential equations modeling pricing under uncertainty. Zbl 1336.35348Coclite, G. M.; Reichmann, O.; Risebro, N. H. 2 2016 Convergence of front tracking and the Glimm scheme for a model of the flow of immiscible gases. Zbl 1404.65119Holden, Helge; Risebro, Nils Henrik; Sande, Hilde 1 2009 Finite difference schemes for the symmetric Keyfitz-Kranzer system. Zbl 1277.65070Koley, Ujjwal; Risebro, Nils Henrik 1 2013 Operator splitting for convection-dominated nonlinear partial differential equations. Zbl 0989.65093Holden, Helge; Karlsen, Kenneth Hvistendahl; Lie, Knut-Andreas; Risebro, Nils Henrik 1 2001 Reservoir simulation by front tracking. Zbl 0976.35509Gimse, T.; Holden, H.; Risebro, N. H. 1 1996 Well-posedness of a \(2\times 2\) system of resonant conservation laws. Zbl 0931.35094Klausen, Runhild Aae; Risebro, Nils Henrik 1 1999 Maximum principles for a class of conservation laws. Zbl 0843.35056Holden, Helge; Risebro, Nils Henrik; Tveito, Aslak 1 1995 Semi-Godunov schemes for general triangular systems of conservation laws. Zbl 1133.76033Karlsen, Kenneth Hvistendahl; Mishra, Siddhartha; Risebro, Nils Henrik 1 2008 A note on the convergence of a Crank-Nicolson scheme for the KdV equation. Zbl 1401.65104Dutta, Rajib; Risebro, Nils Henrik 1 2016 Correction to: “Multilevel Monte Carlo front-tracking for random scalar conservation laws”. Zbl 1430.65004Risebro, Nils Henrik; Schwab, Christoph; Weber, Franziska 1 2018 Numerical methods for conservation laws with rough flux. Zbl 1437.35485Hoel, H.; Karlsen, K. H.; Risebro, N. H.; Storrøsten, E. B. 1 2020 Models for dense multilane vehicular traffic. Zbl 1441.35162Holden, Helge; Risebro, Nils Henrik 4 2019 A difference method for the McKean-Vlasov equation. Zbl 1423.35382Coclite, Giuseppe Maria; Risebro, Nils Henrik 3 2019 The continuum limit of follow-the-leader models – a short proof. Zbl 1378.35180Holden, Helge; Risebro, Nils Henrik 13 2018 Follow-the-leader models can be viewed as a numerical approximation to the Lighthill-Whitham-Richards model for traffic flow. Zbl 1414.35122Holden, Helge; Risebro, Nils Henrik 8 2018 Path-dependent convex conservation laws. Zbl 1402.35170Hoel, H.; Karlsen, K. H.; Risebro, N. H.; Storrøsten, E. B. 4 2018 Correction to: “Multilevel Monte Carlo front-tracking for random scalar conservation laws”. Zbl 1430.65004Risebro, Nils Henrik; Schwab, Christoph; Weber, Franziska 1 2018 A convergent finite difference scheme for the Ostrovsky-Hunter equation on a bounded domain. Zbl 1368.65133Coclite, G. M.; Ridder, J.; Risebro, N. H. 12 2017 A multilevel Monte Carlo finite difference method for random scalar degenerate convection-diffusion equations. Zbl 1373.35179Koley, Ujjwal; Risebro, Nils Henrik; Schwab, Christoph; Weber, Franziska 8 2017 Practical convergence rates for degenerate parabolic equations. Zbl 1372.35166Karlsen, Kenneth H.; Risebro, Nils H.; Storrøsten, E. B. 1 2017 Numerical solution of scalar conservation laws with random flux functions. Zbl 1343.65007Mishra, Siddhartha; Risebro, Nils Henrik; Schwab, Christoph; Tokareva, Svetlana 16 2016 Multilevel Monte Carlo front-tracking for random scalar conservation laws. Zbl 1350.65008Risebro, Nils Henrik; Schwab, Christoph; Weber, Franziska 6 2016 On the convergence rate of finite difference methods for degenerate convection-diffusion equations in several space dimensions. Zbl 1342.65182Karlsen, Kenneth Hvistendahl; Risebro, Nils Henrik; Storrøsten, Erlend Briseid 5 2016 Convergence of finite difference schemes for the Benjamin-Ono equation. Zbl 1353.65090Dutta, Rajib; Holden, Helge; Koley, Ujjwal; Risebro, Nils Henrik 3 2016 A convergent difference scheme for a class of partial integro-differential equations modeling pricing under uncertainty. Zbl 1336.35348Coclite, G. M.; Reichmann, O.; Risebro, N. H. 2 2016 A note on the convergence of a Crank-Nicolson scheme for the KdV equation. Zbl 1401.65104Dutta, Rajib; Risebro, Nils Henrik 1 2016 Front tracking for hyperbolic conservation laws. 2nd edition. Zbl 1346.35004Holden, Helge; Risebro, Nils Henrik 52 2015 Convergence of a fully discrete finite difference scheme for the Korteweg-de Vries equation. Zbl 1348.65121Holden, Helge; Koley, Ujjwal; Risebro, Nils Henrik 11 2015 Convergence of a higher order scheme for the Korteweg-de Vries equation. Zbl 1342.35301Dutta, Rajib; Koley, Ujjwal; Risebro, Nils Henrik 7 2015 Operator splitting for the Benjamin-Ono equation. Zbl 1326.35311Dutta, R.; Holden, H.; Koley, U.; Risebro, N. H. 4 2015 \(L^{1}\) error estimates for difference approximations of degenerate convection-diffusion equations. Zbl 1300.65067Karlsen, K. H.; Risebro, N. H.; Storrøsten, E. B. 9 2014 Analysis and numerical approximation of Brinkman regularization of two-phase flows in porous media. Zbl 1392.76075Coclite, G. M.; Mishra, S.; Risebro, N. H.; Weber, F. 6 2014 On an inverse problem for scalar conservation laws. Zbl 1286.35266Holden, Helge; Priuli, Fabio Simone; Risebro, Nils Henrik 3 2014 Convergence of a relaxation scheme for a \(2\times 2\) triangular system of conservation laws. Zbl 1320.65127Agrell, Christian; Risebro, Nils Henrik 1 2014 Operator splitting for partial differential equations with Burgers nonlinearity. Zbl 1260.35184Holden, Helge; Lubich, Christian; Risebro, Nils Henrik 28 2013 Finite difference schemes for the symmetric Keyfitz-Kranzer system. Zbl 1277.65070Koley, Ujjwal; Risebro, Nils Henrik 1 2013 A note on front tracking for the Keyfitz-Kranzer system. Zbl 1316.35192Risebro, N. H.; Weber, F. 1 2013 An error estimate for the finite difference approximation to degenerate convection-diffusion equations. Zbl 1248.65098Karlsen, K. H.; Koley, U.; Risebro, N. H. 11 2012 Higher-order finite difference schemes for the magnetic induction equations with resistivity. Zbl 1252.78033Koley, U.; Mishra, S.; Risebro, N. H.; Svärd, M. 11 2012 A hyperbolic-elliptic model of two-phase flow in porous media-existence of entropy solutions. Zbl 1277.76100Coclite, G. M.; Karlsen, K. H.; Mishra, S.; Risebro, N. H. 5 2012 A theory of \(L ^{1}\)-dissipative solvers for scalar conservation laws with discontinuous flux. Zbl 1261.35088Andreianov, Boris; Karlsen, Kenneth Hvistendahl; Risebro, Nils Henrik 68 2011 Operator splitting for the KdV equation. Zbl 1219.35235Holden, Helge; Karlsen, Kenneth H.; Risebro, Nils Henrik; Tao, Terence 29 2011 Front tracking for hyperbolic conservation laws. Paperback ed. Zbl 1239.35003Holden, Helge; Risebro, Nils Henrik 22 2011 Approximate Riemann solvers and robust high-order finite volume schemes for multi-dimensional ideal MHD equations. Zbl 1364.76113Fuchs, Franz Georg; McMurry, Andrew D.; Mishra, Siddhartha; Risebro, Nils Henrik; Waagan, Knut 13 2011 Splitting methods for partial differential equations with rough solutions. Analysis and Matlab programs. Zbl 1191.35005Holden, Helge; Karlsen, Kenneth H.; Lie, Knut-Andreas; Risebro, Nils Henrik 53 2010 On vanishing viscosity approximation of conservation laws with discontinuous flux. Zbl 1270.35305Andreianov, Boris; Karlsen, Kenneth H.; Risebro, Nils H. 27 2010 Convergence of an Engquist-Osher scheme for a multi-dimensional triangular system of conservation laws. Zbl 1369.65108Coclite, G. M.; Mishra, S.; Risebro, N. H. 9 2010 High-order well-balanced finite volume schemes for simulating wave propagation in stratified magnetic atmospheres. Zbl 1190.76153Fuchs, F. G.; McMurry, A. D.; Mishra, S.; Risebro, N. H.; Waagan, K. 8 2010 Front tracking for a model of immiscible gas flow with large data. Zbl 1425.76214Holden, Helge; Risebro, Nils Henrik; Sande, Hilde 7 2010 Finite volume methods for wave propagation in stratified magneto-atmospheres. Zbl 1364.76114Fuchs, Franz Georg; Mcmurry, Andrew D.; Mishra, Siddhartha; Risebro, Nils Henrik; Waagan, Knut 1 2010 Stable upwind schemes for the magnetic induction equation. Zbl 1177.78057Fuchs, Franz G.; Karlsen, Kenneth H.; Mishra, Siddharta; Risebro, Nils H. 15 2009 The solution of the Cauchy problem with large data for a model of a mixture of gases. Zbl 1178.35248Holden, Helge; Risebro, Nils Henrik; Sande, Hilde 12 2009 Convergence of finite volume schemes for triangular systems of conservation laws. Zbl 1190.65133Karlsen, Kenneth Hvistendahl; Mishra, Siddhartha; Risebro, Nils Henrik 11 2009 Higher order finite difference schemes for the magnetic induction equations. Zbl 1168.78317Koley, Ujjwal; Mishra, Siddhartha; Risebro, Nils Henrik; Svärd, Magnus 11 2009 Splitting based finite volume schemes for ideal MHD equations. Zbl 1259.76021Fuchs, F. G.; Mishra, S.; Risebro, N. H. 10 2009 A convergent finite-difference method for a nonlinear variational wave equation. Zbl 1236.65112Holden, H.; Karlsen, K. H.; Risebro, N. H. 8 2009 An introduction to the theory of scalar conservation laws with spatially discontinuous flux functions. Zbl 1191.74032Risebro, Nils Henrik 7 2009 Well-balanced schemes for conservation laws with source terms based on a local discontinuous flux formulation. Zbl 1198.35149Karlsen, Kenneth Hvistendahl; Mishra, Siddhartha; Risebro, Nils Henrik 6 2009 Semi-Godunov schemes for multiphase flows in porous media. Zbl 1191.35022Karlsen, K. H.; Mishra, S.; Risebro, N. H. 5 2009 Convergence of vanishing viscosity approximations of \(2\times 2\) triangular systems of multi-dimensional conservation laws. Zbl 1178.35246Coclite, G. M.; Karlsen, K. H.; Mishra, S.; Risebro, N. H. 4 2009 Convergence of front tracking and the Glimm scheme for a model of the flow of immiscible gases. Zbl 1404.65119Holden, Helge; Risebro, Nils Henrik; Sande, Hilde 1 2009 Numerical schemes for computing discontinuous solutions of the Degasperis-Procesi equation. Zbl 1246.76114Coclite, G. M.; Karlsen, K. H.; Risebro, N. H. 28 2008 A convergent finite difference scheme for the Camassa–Holm equation with general \(H^1\) initial data. Zbl 1172.35310Coclite, G. M.; Karlsen, K. H.; Risebro, N. H. 20 2008 An explicit finite difference scheme for the Camassa-Holm equation. Zbl 1191.35021Coclite, Giuseppe Maria; Karlsen, Kenneth H.; Risebro, Nils Henrik 9 2008 Semi-Godunov schemes for general triangular systems of conservation laws. Zbl 1133.76033Karlsen, Kenneth Hvistendahl; Mishra, Siddhartha; Risebro, Nils Henrik 1 2008 Convergent difference schemes for the Hunter–Saxton equation. Zbl 1114.65101Holden, H.; Karlsen, K. H.; Risebro, N. H. 14 2007 Viscosity solutions of Hamilton-Jacobi equations with discontinuous coefficients. Zbl 1144.35016Coclite, Giuseppe Maria; Risebro, Nils Henrik 9 2007 Conservation laws with time dependent discontinuous coefficients. Zbl 1078.35071Coclite, Giuseppe Maria; Risebro, Nils Henrik 22 2005 A relaxation scheme for continuous sedimentation in ideal clarifier-thickener units. Zbl 1122.76063Bürger, R.; Karlsen, K. H.; Risebro, N. H. 10 2005 Well-posedness in \(BV_t\) and convergence of a difference scheme for continuous sedimentation in ideal clarifier-thickener units. Zbl 1053.76047Bürger, R.; Karlsen, K. H.; Risebro, N. H.; Towers, J. D. 52 2004 Monotone difference approximations for the simulation of clarifier-thickener units. Zbl 1299.76283Bürger, R.; Karlsen, K. H.; Risebro, N. H.; Towers, J. D. 14 2004 A relaxation scheme for conservation laws with a discontinuous coefficient. Zbl 1078.65076Karlsen, K. H.; Klingenberg, C.; Risebro, N. H. 10 2004 Front tracking for scalar balance equations. Zbl 1053.35088Karlsen, K. H.; Risebro, N. H.; Towers, J. D. 6 2004 \(L^1\) stability for entropy solutions of nonlinear degenerate parabolic convection-diffusion equations with discontinuous coefficients. Zbl 1036.35104Karlsen, K. H.; Risebro, N. H.; Towers, J. D. 65 2003 On the uniqueness and stability of entropy solutions of nonlinear degenerate parabolic equations with rough coefficients. Zbl 1027.35057Karlsen, Kenneth Hvistendahl; Risebro, Nils Henrik 62 2003 A front tracking approach to a model of continuous sedimentation in ideal clarifier-thickener units. Zbl 1013.35052Bürger, R.; Karlsen, K. H.; Klingenberg, C.; Risebro, N. H. 25 2003 When are HJB-equations in stochastic control of delay systems finite dimensional? Zbl 1052.60051Larssen, Bjørnar; Risebro, Nils Henrik 23 2003 On uniqueness and existence of entropy solutions of weakly coupled systems of nonlinear degenerate parabolic equations. Zbl 1036.35102Holden, Helge; Karlsen, Kenneth H.; Risebro, Nils H. 8 2003 On a model for continuous sedimentation in vessels with discontinuous cross-sectional area. Zbl 1059.76542Bürger, R.; Karlsen, K. H.; Risebro, N. H.; Towers, J. D. 6 2003 Front tracking for hyperbolic conservation laws. Zbl 1006.35002Holden, Helge; Risebro, Nils Henrik 89 2002 Upwind difference approximations for degenerate parabolic convection-diffusion equations with a discontinuous coefficient. Zbl 1014.65073Karlsen, K. H.; Risebro, N. H.; Towers, J. D. 53 2002 On a nonlinear degenerate parabolic transport-diffusion equation with a discontinuous coefficient. Zbl 1015.35049Karlsen, Kenneth H.; Risebro, Nils H.; Towers, John D. 17 2002 A note on front tracking and the equivalence between viscosity solutions of Hamilton-Jacobi equations and entropy solutions of scalar conservation laws. Zbl 1010.35026Karlsen, Kenneth Hvistendahl; Risebro, Nils Henrik 13 2002 Unconditionally stable methods for Hamilton-Jacobi equations. Zbl 1143.65365Karlsen, Kenneth Hvistendahl; Risebro, Nils Henrik 9 2002 Convergence of finite difference schemes for viscous and inviscid conservation laws with rough coefficients. Zbl 1032.76048Karlsen, Kenneth Hvistendahl; Risebro, Nils Henrik 32 2001 Stability of a resonant system of conservation laws modeling polymer flow with gravitation. Zbl 0977.35083Klingenberg, Christian; Risebro, Nils Henrik 27 2001 On the convergence rate of operator splitting for Hamilton-Jacobi equations with source terms. Zbl 1059.70012Jakobsen, Espen Robstad; Karlsen, Kenneth Hvistendahl; Risebro, Nils Henrik 13 2001 Operator splitting for convection-dominated nonlinear partial differential equations. Zbl 0989.65093Holden, Helge; Karlsen, Kenneth Hvistendahl; Lie, Knut-Andreas; Risebro, Nils Henrik 1 2001 Corrected operator splitting for nonlinear parabolic equations. Zbl 0951.35080Karlsen, Kenneth Hvistendahl; Risebro, Nils Henrik 12 2000 A fast marching method for reservoir simulation. Zbl 0997.76062Karlsen, K. Hvistendahl; Lie, K.-A.; Risebro, N. H. 8 2000 Front tracking and operator splitting for nonlinear degenerate convection-diffusion equations. Zbl 0961.65073Evje, S.; Karlsen, K. Hvistendahl; Lie, K. A.; Risebro, N. H. 6 2000 Stability of conservation laws with discontinuous coefficients. Zbl 0935.35097Klausen, Runhild Aae; Risebro, Nils Henrik 32 1999 Operator splitting methods for generalized Korteweg-de Vries equations. Zbl 0947.65102Holden, Helge; Karlsen, Kenneth Hvistendahl; Risebro, Nils Henrik 23 1999 An unconditionally stable method for the Euler equations. Zbl 0922.76251Holden, Helge; Lie, Knut-Andreas; Risebro, Nils Henrik 12 1999 Riemann problems with a kink. Zbl 0926.35087Holden, Helge; Risebro, Nils Henrik 10 1999 A front tracking method for conservation laws with boundary conditions. Zbl 0928.35098Hvistendahl, K.; Lie, K.-A.; Risebro, N. H. 3 1999 Well-posedness of a \(2\times 2\) system of resonant conservation laws. Zbl 0931.35094Klausen, Runhild Aae; Risebro, Nils Henrik 1 1999 Continuous dependence in the large for some equations of gas dynamics. Zbl 0927.35082Colombo, Rinaldo M.; Risebro, Nils H. 11 1998 Conservation laws with a random source. Zbl 0885.35069Holden, H.; Risebro, N. H. 29 1997 An operator splitting method for nonlinear convection-diffusion equations. Zbl 0882.35074Karlsen, Kenneth Hvistendahl; Risebro, Nils Henrik 21 1997 Reservoir simulation by front tracking. Zbl 0976.35509Gimse, T.; Holden, H.; Risebro, N. H. 1 1996 A mathematical model of traffic flow on a network of unidirectional roads. Zbl 0833.35089Holden, Helge; Risebro, Nils Henrik 70 1995 Convex conservation laws with discontinuous coefficients. Existence, uniqueness and asymptotic behavior. Zbl 0836.35090Klingenberg, Christian; Risebro, Nils Henrik 62 1995 Maximum principles for a class of conservation laws. Zbl 0843.35056Holden, Helge; Risebro, Nils Henrik; Tveito, Aslak 1 1995 A front-tracking alternative to the random choice method. Zbl 0799.35153Risebro, Nils Henrik 26 1993 A method of fractional steps for scalar conservation laws without the CFL conditions. Zbl 0799.35150Holden, Helge; Risebro, Nils Henrik 10 1993 FRONTLINE and FRONTSIM: Two full scale, two-phase, black oil reservoir simulators based on front tracking. Zbl 0780.76073Bratvedt, Frode; Bratvedt, Kyrre; Buchholz, Christian F.; Gimse, Tore; Holden, Helge; Holden, Lars; Risebro, Nils Henrik 7 1993 A conservative front tracking scheme for 1D hyperbolic conservation laws. Zbl 0964.65517Langseth, Jan Olav; Risebro, Nils Henrik; Tveito, Aslak 4 1993 Solution of the Cauchy problem for a conservation law with a discontinuous flux function. Zbl 0776.35034Gimse, Tore; Risebro, Nils Henrik 74 1992 A front tracking method for conservation laws in one dimension. Zbl 0756.65120Risebro, N. H.; Tveito, A. 15 1992 ...and 5 more Documents all cited Publications top 5 cited Publications all top 5 Cited by 1,106 Authors 56 Risebro, Nils Henrik 54 Karlsen, Kenneth Hvistendahl 32 Coclite, Giuseppe Maria 28 Bürger, Raimund 27 Mishra, Siddhartha 24 Holden, Helge 23 Colombo, Rinaldo M. 19 Goatin, Paola 18 Andreianov, Boris 17 Piccoli, Benedetto 15 Koley, Ujjwal 13 Diehl, Stefan 13 Herty, Michael Matthias 13 Rosini, Massimiliano Daniele 13 Shen, Wen 12 Garavello, Mauro 12 Towers, John D. 11 Amadori, Debora 11 Klingenberg, Christian 10 Göttlich, Simone 10 Jakobsen, Espen Robstad 9 Chen, Gui-Qiang G. 9 Gowda, G. D. Veerappa 9 Ostermann, Alexander 9 Raynaud, Xavier 8 Adimurthi, A. 8 Bressan, Alberto 8 Corli, Andrea 8 Di Ruvo, Lorenzo 8 Fjordholm, Ulrik Skre 8 Frid, Hermano 8 Rohde, Christian 8 Schwab, Christoph 7 Ancona, Fabio 7 Donadello, Carlotta 7 Evje, Steinar 7 Gess, Benjamin 7 Wang, Guodong 6 Berres, Stefan 6 Cancès, Clément 6 Geiser, Jürgen 6 Lie, Knut-Andreas 6 Majee, Ananta K. 6 Rossi, Elena 6 Ruiz-Baier, Ricardo 6 Sepúlveda, Mauricio A. 6 Shen, Chun 6 Storrøsten, Erlend Briseid 6 Weber, Franziska 6 Wu, Xinglong 5 Abreu, Eduardo 5 Asakura, Fumioki 5 Bauzet, Caroline 5 Biswas, Imran H. 5 Chalons, Christophe 5 Christoforou, Cleopatra C. 5 Cifani, Simone 5 Csomós, Petra 5 Dutta, Rajib 5 Gosse, Laurent 5 Grunert, Katrin 5 Guerra, Graziano 5 Hofmanová, Martina 5 LeFloch, Philippe Gerard 5 Marcellini, Francesca 5 Panov, Evgeniy Yu. 5 Ridder, Johanna 5 Ruf, Adrian M. 5 Sarkar, Tanmay 5 Schratz, Katharina 5 Shu, Chi-Wang 5 Sun, Meina 5 Svärd, Magnus 5 Tadmor, Eitan 5 Tian, Lixin 5 Vallet, Guy 5 Wang, Hong 4 Bayen, Alexandre M. 4 Bretti, Gabriella 4 Briani, Maya 4 Chandrashekar, Praveen 4 Cristiani, Emiliano 4 D’Apice, Ciro 4 Di Francesco, Marco 4 Einkemmer, Lukas 4 Flåtten, Tore 4 Ghoshal, Shyam Sundar 4 Gugat, Martin 4 Hu, Yanbo 4 Jerez, Silvia 4 Klar, Axel 4 Kröker, Ilja 4 Leugering, Günter 4 Li, Yachun 4 Liu, Jianguo 4 Liu, Yue 4 Mitrovic, Darko 4 Saad, Mazen 4 Schlachter, Louisa 4 Schleper, Veronika ...and 1,006 more Authors all top 5 Cited in 188 Serials 54 Journal of Differential Equations 53 Journal of Computational Physics 30 Journal of Mathematical Analysis and Applications 30 Networks and Heterogeneous Media 28 Journal of Hyperbolic Differential Equations 27 Journal of Computational and Applied Mathematics 26 Applied Numerical Mathematics 24 Mathematics of Computation 24 Applied Mathematics and Computation 21 Numerische Mathematik 21 Journal of Scientific Computing 19 European Series in Applied and Industrial Mathematics (ESAIM): Mathematical Modelling and Numerical Analysis 18 SIAM Journal on Numerical Analysis 17 BIT 16 Archive for Rational Mechanics and Analysis 15 Computers & Mathematics with Applications 14 ZAMP. 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