Edit Profile LeFloch, Philippe Gerard Compute Distance To: Compute Author ID: lefloch.philippe-g Published as: Le Floch, Ph.; Le Floch, Philippe; Le Floch, Philippe G.; LeFloch, P. G.; LeFloch, Philippe; LeFloch, Philippe G.; LeFloch, Philippe Gerard; LeFloch, Phillippe; Lefloch, Philippe; Lefloch, Philippe G. Homepage: https://philippelefloch.org/ External Links: MGP · arXiv Documents Indexed: 216 Publications since 1985, including 3 Books all top 5 Co-Authors 26 single-authored 13 Coquel, Frédéric 8 Bedjaoui, Nabil 8 Mai Duc Thanh 7 Joseph, Kayyunnapara Thomas 7 Rohde, Christian 6 Amorim, Paulo 6 Boutin, Benjamin 6 Chalons, Christophe 6 Chen, Gui-Qiang G. 5 Baiti, Paolo 5 Beyer, Florian 5 Ma, Yue 5 Okutmustur, Baver 5 Piccoli, Benedetto 4 Colombo, Rinaldo M. 4 Goatin, Paola 4 Hayes, Brian T. 4 Mishra, Siddhartha 4 Raviart, Pierre-Arnaud 4 Smulevici, Jacques 4 Xiang, Shuyang 3 Ames, Ellery 3 Ben-Artzi, Matania 3 Correia, Joaquim M. C. 3 Dias, João-Paulo 3 Dubois, François 3 Grubic, Nastasia 3 Hou, Thomas Yizhao 3 Isenberg, James A. 3 Mardare, Cristinel 3 Mercier, Jean-Marc 3 Nédélec, Jean-Claude 3 Parés Madroñal, Carlos 2 Beljadid, Abdelaziz 2 Berthon, Christophe 2 Bourgeade, Antoine 2 Bressan, Alberto 2 Burtscher, Annegret Y. 2 Castro, Manuel J. 2 Chen, Binglong 2 Cockburn, Bernardo 2 Dong, Shijie 2 Grant, James D. E. 2 Kondo, Cezar I. 2 Kröner, Dietmar 2 Lagoutière, Frédéric 2 Li, Tatsien 2 Liu, Jianguo 2 Makhlof, Hasan 2 Muñoz-Ruiz, María Luz 2 Neves, Wladimir 2 Stewart, John M. 2 Trivisa, Konstantina 2 Tzavaras, Athanasios E. 2 Wei, Changhua 1 Amadori, Debora 1 Ambrosio, Luigi 1 Ambroso, Annalisa 1 Bakhtin, Yuri Yu. 1 Barnes, A. P. 1 Beig, Robert 1 Bereux, François 1 Bernardi, Christine 1 Bonnetier, Eric 1 Boscarino, Sebastiano 1 Choudhury, Anupam Pal 1 Crasta, Graziano 1 Crippa, Gianluca 1 Dal Maso, Gianni 1 Du, Qiang 1 Ernest, Jan 1 Falcovitz, Joseph 1 Figueira, Mário S. R. 1 Forestier, Alain 1 Frid, Hermano 1 Georgiev, Svetlin Georgiev 1 Germain, Pierre 1 Giesselmann, Jan 1 Glass, Olivier 1 Godlewski, Edwige 1 Hong, John Meng-Kai 1 Hu, Jiaxin 1 Huang, Zhan 1 Iguchi, Tatsuo 1 Jang, Juhi 1 Kissling, Frederike 1 Klingenberg, Christian 1 Laforest, Marc 1 Le Floch, Bruno 1 Lee, Dan Archibald 1 Liu, Tai-Ping 1 Mardare, Sorin 1 Martín-García, José Maria 1 Masmoudi, Nader 1 Mohammadian, Abdolmajid M. 1 Mohammadian, Majid 1 Murat, François 1 Natalini, Roberto 1 Novak, Jérôme 1 Olsson, Fredrik ...and 19 more Co-Authors all top 5 Serials 15 Archive for Rational Mechanics and Analysis 11 Comptes Rendus de l’Académie des Sciences. Série I 9 Journal of Differential Equations 9 SIAM Journal on Numerical Analysis 9 Portugaliae Mathematica. Nova Série 8 Journal of Computational Physics 7 Journal de Mathématiques Pures et Appliquées. Neuvième Série 7 Proceedings of the Royal Society of Edinburgh. Section A. Mathematics 6 Classical and Quantum Gravity 6 Mathematics of Computation 6 Comptes Rendus. Mathématique. Académie des Sciences, Paris 5 Annales de l’Institut Henri Poincaré. Analyse Non Linéaire 5 SIAM Journal on Mathematical Analysis 4 Communications in Mathematical Sciences 4 Oberwolfach Reports 3 Communications in Mathematical Physics 3 Communications on Pure and Applied Mathematics 3 Numerische Mathematik 3 Communications in Partial Differential Equations 3 Communications on Pure and Applied Analysis 3 Journal of Hyperbolic Differential Equations 2 Mathematical Methods in the Applied Sciences 2 ZAMP. Zeitschrift für angewandte Mathematik und Physik 2 Journal of Geometry and Physics 2 Indiana University Mathematics Journal 2 Chinese Annals of Mathematics. Series B 2 Japan Journal of Industrial and Applied Mathematics 2 Matemática Contemporânea 2 Interfaces and Free Boundaries 2 Annales Henri Poincaré 2 European Series in Applied and Industrial Mathematics (ESAIM): Mathematical Modelling and Numerical Analysis 2 Communications in Computational Physics 2 Series in Applied and Computational Mathematics 1 Computer Methods in Applied Mechanics and Engineering 1 Nonlinearity 1 Annali dell’Università di Ferrara. Nuova Serie. Sezione VII 1 Journal of Functional Analysis 1 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods 1 Transactions of the American Mathematical Society 1 RAIRO. Modélisation Mathématique et Analyse Numérique 1 Asymptotic Analysis 1 Forum Mathematicum 1 IMPACT of Computing in Science and Engineering 1 Mémoires de la Société Mathématique de France. Nouvelle Série 1 Journal of Dynamics and Differential Equations 1 Boletim da Sociedade Brasileira de Matemática. Nova Série 1 SIAM Journal on Scientific Computing 1 Communications in Analysis and Geometry 1 Séminaire Équations aux Dérivées Partielles 1 Electronic Journal of Differential Equations (EJDE) 1 NoDEA. Nonlinear Differential Equations and Applications 1 Methods and Applications of Analysis 1 Discrete and Continuous Dynamical Systems 1 Advances in Theoretical and Mathematical Physics 1 Journal of the European Mathematical Society (JEMS) 1 Acta Mathematica Sinica. English Series 1 Far East Journal of Mathematical Sciences 1 Acta Mathematica Scientia. Series B. (English Edition) 1 Analysis and Applications (Singapore) 1 Acta Numerica 1 Bulletin of the Institute of Mathematics. Academia Sinica. New Series 1 Communications in Applied Mathematics and Computational Science 1 Networks and Heterogeneous Media 1 Kinetic and Related Models 1 Analysis & PDE 1 International Journal of Dynamical Systems and Differential Equations 1 Differential Equations and Applications 1 Stochastic and Partial Differential Equations. Analysis and Computations 1 Nonlinear Analysis. Theory, Methods & Applications all top 5 Fields 189 Partial differential equations (35-XX) 97 Fluid mechanics (76-XX) 53 Numerical analysis (65-XX) 40 Relativity and gravitational theory (83-XX) 28 Differential geometry (53-XX) 18 Mechanics of deformable solids (74-XX) 10 Global analysis, analysis on manifolds (58-XX) 4 General and overarching topics; collections (00-XX) 4 Classical thermodynamics, heat transfer (80-XX) 3 Dynamical systems and ergodic theory (37-XX) 3 Calculus of variations and optimal control; optimization (49-XX) 2 Real functions (26-XX) 1 Algebraic geometry (14-XX) 1 Measure and integration (28-XX) 1 Functions of a complex variable (30-XX) 1 Geometry (51-XX) 1 Manifolds and cell complexes (57-XX) 1 Mechanics of particles and systems (70-XX) 1 Quantum theory (81-XX) 1 Statistical mechanics, structure of matter (82-XX) 1 Astronomy and astrophysics (85-XX) 1 Game theory, economics, finance, and other social and behavioral sciences (91-XX) Publications by Year all cited Publications top 5 cited Publications Citations contained in zbMATH Open 181 Publications have been cited 2,625 times in 1,317 Documents Cited by ▼ Year ▼ Definition and weak stability of nonconservative products. Zbl 0853.35068Dal Maso, Gianni; LeFloch, Philippe G.; Murat, François 275 1995 Hyperbolic systems of conservation laws. The theory of classical and nonclassical shock waves. Zbl 1019.35001LeFloch, Philippe G. 142 2002 Boundary conditions for nonlinear hyperbolic systems of conservation laws. Zbl 0649.35057Dubois, François; Le Floch, Philippe 103 1988 Why nonconservative schemes converge to wrong solutions: Error analysis. Zbl 0809.65102Hou, Thomas Y.; Le Floch, Philippe G. 81 1994 Why many theories of shock waves are necessary: convergence error in formally path-consistent schemes. Zbl 1176.76084Castro, Manuel J.; LeFloch, Philippe G.; Muñoz-Ruiz, María Luz; Parés, Carlos 73 2008 The Riemann problem for a class of resonant hyperbolic systems of balance laws. Zbl 1086.35069Goatin, Paola; LeFloch, Philippe G. 53 2004 Non-classical shocks and kinetic relations: Scalar conservation laws. Zbl 0902.76053Hayes, Brian T.; LeFloch, Philippe G. 50 1997 The Riemann problem for fluid flows in a nozzle with discontinuous cross-section. Zbl 1091.35044LeFloch, Philippe G.; Mai Duc Thanh 47 2003 Fully discrete, entropy conservative schemes of arbitrary order. Zbl 1033.65073LeFloch, P. G.; Mercier, J. M.; Rohde, C. 46 2002 Entropy weak solutions to nonlinear hyperbolic systems under nonconservative form. Zbl 0683.35049Le Floch, Philippe 46 1988 The Riemann problem for the shallow water equations with discontinuous topography. Zbl 1145.35082LeFloch, Philippe G.; Thanh, Mai Duc 43 2007 Existence theory for nonlinear hyperbolic systems in nonconservative form. Zbl 0804.35086Le Floch, Philippe; Liu, Tai-Ping 38 1993 A Godunov-type method for the shallow water equations with discontinuous topography in the resonant regime. Zbl 1453.35150LeFloch, Philippe G.; Thanh, Mai Duc 37 2011 Measure solutions to a strictly hyperbolic system of conservation laws. Zbl 0908.35075Hayes, Brian T.; LeFloch, Philippe G. 36 1996 Conservation laws with vanishing nonlinear diffusion and dispersion. Zbl 0923.35159LeFloch, Philippe G.; Natalini, Roberto 35 1999 Convergence of the finite volume method for multidimensional conservation laws. Zbl 0845.65051Cockburn, B.; Coquel, F.; LeFloch, P. G. 35 1995 An error estimate for finite volume methods for multidimensional conservation laws. Zbl 0855.65103Cockburn, Bernardo; Coquel, Frédéric; LeFloch, Philippe 35 1994 An existence and uniqueness result for two nonstrictly hyperbolic systems. Zbl 0727.35083Le Floch, Philippe 34 1990 Propagating phase boundaries: Formulation of the problem and existence via the Glimm method. Zbl 0784.73010Le Floch, Philippe 33 1993 Representation of weak limits and definition of nonconservative products. Zbl 0939.35115LeFloch, Philippe G.; Tzavaras, Athanasios E. 31 1999 Uniqueness of weak solutions to systems of conservation laws. Zbl 0903.35039Bressan, Alberto; LeFloch, Philippe 31 1997 An asymptotic expansion for the solution of the generalized Riemann problem. I: General theory. Zbl 0679.35064Le Floch, Philippe; Raviart, Pierre-Arnaud 30 1988 Explicit formula for scalar nonlinear conservation laws with boundary condition. Zbl 0679.35065Le Floch, Philippe 29 1988 Existence theory for the isentropic Euler equations. Zbl 1027.76043Chen, Gui-Qiang; LeFloch, Philippe G. 28 2003 Nonclassical shocks and kinetic relations: Strictly hyperbolic systems. Zbl 0953.35095Hayes, Brian T.; LeFloch, Philippe G. 28 2000 Compressible Euler equations with general pressure law. Zbl 0970.76082Chen, Gui-Qiang; LeFloch, Philippe G. 26 2000 An asymptotic expansion for the solution of the generalized Riemann problem. II: Application to the equation of gas dynamics. Zbl 0703.35106Bourgeade, A.; Le Floch, Ph.; Raviart, P. A. 26 1989 The minimum entropy principle for compressible fluid flows in a nozzle with discontinuous cross-section. Zbl 1139.76048Kröner, Dietmar; LeFloch, Philippe G.; Thanh, Mai-Duc 24 2008 Finite energy solutions to the isentropic Euler equations with geometric effects. Zbl 1188.35150LeFloch, Philippe G.; Westdickenberg, Michael 24 2007 High-order schemes, entropy inequalities, and nonclassical shocks. Zbl 0959.35117LeFloch, Philippe G.; Rohde, Christian 23 2000 Structural stability and regularity of entropy solutions to hyperbolic systems of conservation laws. Zbl 0932.35139Bressan, Alberto; LeFloch, Philippe G. 23 1999 Zero diffusion-dispersion limits for scalar conservation laws. Zbl 1055.35072Kondo, Cezar I.; LeFloch, Philippe G. 21 2002 Convergence of finite difference schemes for conservation laws in several space dimensions: The corrected antidiffusive flux approach. Zbl 0741.35036Coquel, Frédéric; Le Floch, Philippe 21 1991 The global nonlinear stability of Minkowski space for self-gravitating massive fields. The wave-Klein-Gordon model. Zbl 1359.83003LeFloch, Philippe G.; Ma, Yue 20 2016 Existence theory for hyperbolic systems of conservation laws with general flux-functions. Zbl 1036.35130Iguchi, Tatsuo; LeFloch, Philippe G. 20 2003 Diffusive-dispersive traveling waves and kinetic relations. I: Nonconvex hyperbolic conservation laws. Zbl 1001.35082Bedjaoui, Nabil; LeFloch, Philippe G. 20 2002 Diffusive-dispersive travelling waves and kinetic relations. II: A hyperbolic-elliptic model of phase-transition dynamics. Zbl 1082.35104Bedjaoui, Nabil; LeFloch, Philippe G. 19 2002 Boundary layers in weak solutions of hyperbolic conservation laws. Zbl 0959.35119Joseph, K. T.; LeFloch, P. G. 19 1999 Nonclassical shocks and kinetic relations: Finite difference schemes. Zbl 0938.35096Hayes, Brian T.; LeFloch, Philippe G. 19 1998 Convergence of finite difference schemes for conservation laws in several space dimensions: A general theory. Zbl 0781.65078Coquel, Frédéric; Le Floch, Philippe 19 1993 The hyperboloidal foliation method. Zbl 1320.53001LeFloch, Philippe G.; Ma, Yue 18 2014 The characteristic initial value problem for plane symmetric spacetimes with weak regularity. Zbl 1222.83028LeFloch, Philippe G.; Stewart, John M. 17 2011 Non-monotonic traveling waves in van der Waals fluids. Zbl 1083.35060Bedjaoui, N.; Chalons, C.; Coquel, F.; LeFloch, P. G. 17 2005 Well-posedness theory for geometry-compatible hyperbolic conservation laws on manifolds. Zbl 1138.35055Ben-Artzi, Matania; LeFloch, Philippe G. 16 2007 Definition and stability of Lorentzian manifolds with distributional curvature. Zbl 1144.35311LeFloch, Philippe G.; Mardare, Cristinel 15 2007 Non-classical Riemann solvers and kinetic relations. II: An hyperbolic-elliptic model of phase-transition dynamics. Zbl 1021.35073LeFloch, Philippe G.; Tanh, Mai Duc 15 2002 Generalized monotone schemes, discrete paths of extrema, and discrete entropy conditions. Zbl 0915.35069LeFloch, Philippe G.; Liu, Jian-Guo 15 1999 Uniqueness via the adjoint problems for systems of conservation laws. Zbl 0797.35116Le Floch, Philippe; Xin, Zhouping 15 1993 The hyperbolic mean curvature flow. Zbl 1159.53025LeFloch, Philippe G.; Smoczyk, Knut 14 2008 Graph solutions of nonlinear hyperbolic systems. Zbl 1071.35078LeFloch, Philippe G. 14 2004 Diffusive-dispersive travelling waves and kinetic relations. V: Singular diffusion and nonlinear dispersion. Zbl 1065.35182Bedjaoui, Nabil; LeFloch, Philippe G. 14 2004 Computational method for propagating phase boundaries. Zbl 0855.73080Zhong, Xiaoguang; Hou, Thomas Y.; LeFloch, Philippe G. 14 1996 Finite energy method for compressible fluids: the Navier-Stokes-Korteweg model. Zbl 1339.35240Germain, Pierre; Lefloch, Philippe 13 2016 High-order asymptotic-preserving methods for fully nonlinear relaxation problems. Zbl 1426.76455Boscarino, Sebastiano; LeFloch, Philippe G.; Russo, Giovanni 13 2014 Late-time/stiff-relaxation asymptotic-preserving approximations of hyperbolic equations. Zbl 1317.65182Berthon, Christophe; LeFloch, Philippe G.; Turpault, Rodolphe 13 2013 A symmetrization of the relativistic Euler equations with several spatial variables. Zbl 1192.35118LeFloch, Philippe G.; Ukai, Seiji 13 2009 Convergent and conservative schemes for nonclassical solutions based on kinetic relations. I. Zbl 1157.65435Boutin, Benjamin; Chalons, Christophe; Lagoutière, Frédéric; LeFloch, Philippe G. 13 2008 A version of the Glimm method based on generalized Riemann problems. Zbl 1125.35003Hong, John M.; LeFloch, Philippe G. 13 2007 Hyperbolic conservation laws on manifolds: total variation estimates and the finite volume method. Zbl 1114.35121Amorim, Paulo; Ben-Artzi, Matania; LeFloch, Philippe G. 13 2005 The Glimm scheme for perfect fluids on plane-symmetric Gowdy spacetimes. Zbl 1080.83011Barnes, A. P.; LeFloch, P. G.; Schmidt, B. G.; Stewart, J. M. 13 2004 An introduction to nonclassical shocks of systems of conservation laws. Zbl 0929.35088LeFloch, Philippe G. 13 1999 A global foliation of Einstein-Euler spacetimes with Gowdy-symmetry on \(T ^{3}\). Zbl 1256.35165LeFloch, Philippe G.; Rendall, Alan D. 12 2011 Hyperbolic conservation laws on the sphere. A geometry-compatible finite volume scheme. Zbl 1168.65372Ben-Artzi, Matania; Falcovitz, Joseph; LeFloch, Philippe G. 12 2009 Lagrangian formulation and a priori estimates for relativistic fluid flows with vacuum. Zbl 1333.35198Jang, Juhi; LeFloch, Philippe G.; Masmoudi, Nader 11 2016 Numerical methods with controlled dissipation for small-scale dependent shocks. Zbl 1398.65211LeFloch, Philippe G.; Mishra, Siddhartha 11 2014 Relativistic Burgers equations on curved spacetimes. Derivation and finite volume approximation. Zbl 1258.35143LeFloch, Philippe G.; Makhlof, Hasan; Okutmustur, Baver 11 2012 Why many theories of shock waves are necessary: kinetic relations for non-conservative systems. Zbl 1234.35190Berthon, Christophe; Coquel, Frédéric; LeFloch, Philippe G. 11 2012 Finite volume schemes on Lorentzian manifolds. Zbl 1179.35027Amorim, Paulo; LeFloch, Philippe G.; Okutmustur, Baver 11 2008 Diffusive-dispersive traveling waves and kinetic relations. IV: Compressible Euler equations. Zbl 1033.35074Bedjaoui, N.; LeFloch, P. G. 11 2003 Diffusive-dispersive traveling waves and kinetic relations. III: An hyperbolic model of elastodynamics. Zbl 1119.35340Bedjaoui, Nabil; LeFloch, Philippe G. 11 2001 Multivalued solutions to some nonlinear and non-strictly hyperbolic systems. Zbl 0768.35058Forestier, Alain; Le Floch, Philippe 11 1992 The global nonlinear stability of Minkowski space for self-gravitating massive fields. Zbl 1434.83005LeFloch, Philippe G.; Ma, Yue 10 2018 Second-order hyperbolic Fuchsian systems and applications. Zbl 1206.83025Beyer, Florian; LeFloch, Philippe G. 10 2010 Boundary layers in weak solutions of hyperbolic conservation laws. II: Self-similar vanishing diffusion limits. Zbl 1020.35055Joseph, K. T.; LeFloch, Philippe G. 10 2002 High-order entropy-conservative schemes and kinetic relations for van der Waals fluids. Zbl 1074.76583Chalons, C.; LeFloch, P. G. 10 2001 Nonclassical Riemann solvers and kinetic relations III: A nonconvex hyperbolic model for Van der Waals fluids. Zbl 0962.35121LeFloch, Philippe G.; Mai Duc Thanh 10 2000 A level-set approach to the computation of twinning and phase-transition dynamics. Zbl 0936.74052Hou, Thomas Y.; Rosakis, Phoebus; LeFloch, Philippe 10 1999 Hyperbolic conservation laws on space-times. A finite volume scheme based on differential forms. Zbl 1178.35250LeFloch, Philippe G.; Okutmustur, Baver 9 2008 Why many theories of shock waves are necessary: Kinetic functions, equivalent equations, and fourth-order models. Zbl 1264.76055LeFloch, Philippe G.; Mohammadian, Majid 9 2008 Properties of Rankine-Hugoniot curves for van der Waals fluids. Zbl 1044.76029LeFloch, Philippe G.; Mai Duc Thanh 9 2003 Computing undercompressive waves with the random choice scheme. Nonclassical shock waves. Zbl 1038.35134Chalons, C.; LeFloch, P. G. 9 2003 Boundary layers in weak solutions of hyperbolic conservation laws. III: Vanishing relaxation limits. Zbl 1021.35065Joseph, K. T.; LeFloch, P. G. 9 2002 Weakly regular fluid flows with bounded variation on the domain of outer communication of a Schwarzschild black hole spacetime. Zbl 1354.35105LeFloch, Philippe G.; Xiang, Shuyang 8 2016 The positive mass theorem for manifolds with distributional curvature. Zbl 1330.53062Lee, Dan A.; LeFloch, Philippe G. 8 2015 The nonlinear stability of rotationally symmetric spaces with low regularity. Zbl 1316.53058LeFloch, Philippe G.; Sormani, Christina 8 2015 Quasilinear hyperbolic Fuchsian systems and AVTD behavior in \(T ^{2}\)-symmetric vacuum spacetimes. Zbl 1272.83009Ames, Ellery; Beyer, Florian; Isenberg, James; LeFloch, Philippe G. 8 2013 Kinetic relations for undercompressive shock waves. Physical, mathematical, and numerical issues. Zbl 1221.35235LeFloch, Philippe G. 8 2010 Injectivity radius of Lorentzian manifolds. Zbl 1156.53040Chen, Bing-Long; LeFloch, Philippe G. 8 2008 Nonclassical Riemann solvers and kinetic relations. I: A nonconvex hyperbolic model of phase transitions. Zbl 1020.35056LeFloch, Philippe G.; Mai Duc Thanh 8 2001 \(L^1\) continuous dependence property for systems of conservation laws. Zbl 1021.35064Hu, Jiaxin; LeFloch, Philippe G. 8 2000 Weakly regular Einstein-Euler spacetimes with Gowdy symmetry: the global areal foliation. Zbl 1266.83027Grubic, Nastasia; LeFloch, Philippe G. 7 2013 Hyperbolic conservation laws on manifolds. An error estimate for finite volume schemes. Zbl 1178.35251LeFloch, Philippe G.; Okutmustur, Baver; Neves, Wladimir 7 2009 Symmetries and global solvability of the isothermal gas dynamics equations. Zbl 1178.76302LeFloch, Philippe G.; Shelukhin, Vladimir 7 2005 Existence result for a class of nonconservative and nonstrictly hyperbolic systems. Zbl 1031.35096Crasta, Graziano; LeFloch, Philippe G. 7 2002 Uniqueness of classical and nonclassical solutions for nonlinear hyperbolic systems. Zbl 0987.35101Baiti, Paolo; LeFloch, Philippe G.; Piccoli, Benedetto 7 2001 Nonlinear diffusive-dispersive limits for multidimensional conservation laws. Zbl 0929.35086Correia, Joaquim M. C.; LeFloch, Philippe G. 7 1998 An entropy satisfying MUSCL scheme for systems of conservation laws. Zbl 0860.65076Coquel, Frédéric; LeFloch, Philippe G. 7 1996 A geometry-preserving finite volume method for compressible fluids on Schwarzschild spacetime. Zbl 1373.76135Le Floch, Philippe G.; Makhlof, Hasan 6 2014 The formation of trapped surfaces in spherically-symmetric Einstein-Euler spacetimes with bounded variation. Zbl 1302.83004Burtscher, Annegret Y.; LeFloch, Philippe G. 6 2014 The equations of elastostatics in a Riemannian manifold. Zbl 1307.74019Grubic, Nastasia; LeFloch, Philippe G.; Mardare, Cristinel 6 2014 Weakly regular fluid flows with bounded variation on the domain of outer communication of a Schwarzschild black hole spacetime. II. Zbl 1411.35201LeFloch, Philippe G.; Xiang, Shuyang 2 2019 The global nonlinear stability of Minkowski space for self-gravitating massive fields. Zbl 1434.83005LeFloch, Philippe G.; Ma, Yue 10 2018 Boundedness of the total energy of relativistic membranes evolving in a curved spacetime. Zbl 1390.35357LeFloch, Philippe G.; Wei, Changhua 2 2018 Ergodicity and Hopf-Lax-Oleinik formula for fluid flows evolving around a black hole under a random forcing. Zbl 1421.35362Bakhtin, Yuri; LeFloch, Philippe G. 1 2018 Self-gravitating fluid flows with Gowdy symmetry near cosmological singularities. Zbl 1382.35299Beyer, Florian; LeFloch, Philippe G. 4 2017 Schemes with well-controlled dissipation. hyperbolic systems in nonconservative form. Zbl 1373.76155Beljadid, Abdelaziz; Lefloch, Philippe G.; Mishra, Siddhartha; Parés, Carlos 4 2017 Nonlocal conservation laws. A new class of monotonicity-preserving models. Zbl 1377.35196Du, Qiang; Huang, Zhan; LeFloch, Philippe G. 2 2017 A class of solutions to the Einstein equations with AVTD behavior in generalized wave gauges. Zbl 1376.83006Ames, Ellery; Beyer, Florian; Isenberg, James; LeFloch, Philippe G. 2 2017 A new method for solving Kolmogorov equations in mathematical finance. Zbl 1419.91651LeFloch, Philippe G.; Mercier, Jean-Marc 1 2017 The mathematical validity of the \(f(R)\) theory of modified gravity. Zbl 1372.83003LeFloch, Philippe G.; Ma, Yue 1 2017 The global nonlinear stability of Minkowski space for self-gravitating massive fields. The wave-Klein-Gordon model. Zbl 1359.83003LeFloch, Philippe G.; Ma, Yue 20 2016 Finite energy method for compressible fluids: the Navier-Stokes-Korteweg model. Zbl 1339.35240Germain, Pierre; Lefloch, Philippe 13 2016 Lagrangian formulation and a priori estimates for relativistic fluid flows with vacuum. Zbl 1333.35198Jang, Juhi; LeFloch, Philippe G.; Masmoudi, Nader 11 2016 Weakly regular fluid flows with bounded variation on the domain of outer communication of a Schwarzschild black hole spacetime. Zbl 1354.35105LeFloch, Philippe G.; Xiang, Shuyang 8 2016 Future asymptotics and geodesic completeness of polarized T2-symmetric spacetimes. Zbl 1342.83010Lefloch, Philippe; Smulevici, Jacques 5 2016 The global nonlinear stability of Minkowski space for the Einstein equations in the presence of a massive field. Zbl 1347.83008LeFloch, Philippe G.; Ma, Yue 4 2016 Weakly regular \(T^2\)-symmetric spacetimes. The future causal geometry of Gowdy spacetimes. Zbl 1331.35341LeFloch, Philippe G.; Smulevici, Jacques 2 2016 The positive mass theorem for manifolds with distributional curvature. Zbl 1330.53062Lee, Dan A.; LeFloch, Philippe G. 8 2015 The nonlinear stability of rotationally symmetric spaces with low regularity. Zbl 1316.53058LeFloch, Philippe G.; Sormani, Christina 8 2015 On the area of the symmetry orbits in weakly regular Einstein-Euler spacetimes with Gowdy symmetry. Zbl 1320.83022Grubic, Nastasia; LeFloch, Philippe G. 4 2015 Weakly regular \(T^2\)-symmetric spacetimes. The global geometry of future Cauchy developments. Zbl 1321.83010LeFloch, Philippe G.; Smulevici, Jacques 4 2015 Coupling techniques for nonlinear hyperbolic equations. IV: Well-balanced schemes for scalar multi-dimensional and multi-component laws. Zbl 1310.65097Boutin, Benjamin; Coquel, Frédéric; LeFloch, Philippe G. 3 2015 Revisiting the method of characteristics via a convex hull algorithm. Zbl 1349.76623LeFloch, Philippe G.; Mercier, Jean-Marc 1 2015 Existence and uniqueness results for the pressureless Euler-Poisson system in one spatial variable. Zbl 1343.35162LeFloch, Philippe G.; Xiang, Shuyang 1 2015 The mathematical theory of self-similar boundary layers for nonlinear hyperbolic systems with viscosity and capillarity. Zbl 1343.35160Choudhury, Anupam Pal; Joseph, K. T.; LeFloch, Philippe G. 1 2015 Schemes with well-controlled dissipation. Zbl 1318.65049Ernest, Jan; LeFloch, Philippe G.; Mishra, Siddhartha 1 2015 The hyperboloidal foliation method. Zbl 1320.53001LeFloch, Philippe G.; Ma, Yue 18 2014 High-order asymptotic-preserving methods for fully nonlinear relaxation problems. Zbl 1426.76455Boscarino, Sebastiano; LeFloch, Philippe G.; Russo, Giovanni 13 2014 Numerical methods with controlled dissipation for small-scale dependent shocks. Zbl 1398.65211LeFloch, Philippe G.; Mishra, Siddhartha 11 2014 A geometry-preserving finite volume method for compressible fluids on Schwarzschild spacetime. Zbl 1373.76135Le Floch, Philippe G.; Makhlof, Hasan 6 2014 The formation of trapped surfaces in spherically-symmetric Einstein-Euler spacetimes with bounded variation. Zbl 1302.83004Burtscher, Annegret Y.; LeFloch, Philippe G. 6 2014 The equations of elastostatics in a Riemannian manifold. Zbl 1307.74019Grubic, Nastasia; LeFloch, Philippe G.; Mardare, Cristinel 6 2014 Null injectivity estimate under an upper bound on the curvature. Zbl 1334.53075Grant, James D. E.; LeFloch, Philippe G. 3 2014 Structure-preserving shock-capturing methods: late-time asymptotics, curved geometry, small-scale dissipation, and nonconservative products. Zbl 1304.76041LeFloch, Philippe G. 1 2014 Late-time/stiff-relaxation asymptotic-preserving approximations of hyperbolic equations. Zbl 1317.65182Berthon, Christophe; LeFloch, Philippe G.; Turpault, Rodolphe 13 2013 Quasilinear hyperbolic Fuchsian systems and AVTD behavior in \(T ^{2}\)-symmetric vacuum spacetimes. Zbl 1272.83009Ames, Ellery; Beyer, Florian; Isenberg, James; LeFloch, Philippe G. 8 2013 Weakly regular Einstein-Euler spacetimes with Gowdy symmetry: the global areal foliation. Zbl 1266.83027Grubic, Nastasia; LeFloch, Philippe G. 7 2013 Quasilinear symmetric hyperbolic Fuchsian systems in several space dimensions. Zbl 1320.35193Ames, Ellery; Beyer, Florian; Isenberg, James; LeFloch, Philippe G. 5 2013 Hyperbolic balance laws with entropy on a curved spacetime: the weak-strong uniqueness theory. Zbl 1288.35344LeFloch, Philippe G. 3 2013 Coupling techniques for nonlinear hyperbolic equations. III: The well-balanced approximation of thick interfaces. Zbl 1371.35172Boutin, Benjamin; Coquel, Frédéric; LeFloch, Philippe G. 3 2013 The linear stability of shock waves for the nonlinear Schrödinger-inviscid Burgers system. Zbl 1307.35271Amorim, Paulo; Dias, João-Paulo; Figueira, Mário; LeFloch, Philippe G. 1 2013 Relativistic Burgers equations on curved spacetimes. Derivation and finite volume approximation. Zbl 1258.35143LeFloch, Philippe G.; Makhlof, Hasan; Okutmustur, Baver 11 2012 Why many theories of shock waves are necessary: kinetic relations for non-conservative systems. Zbl 1234.35190Berthon, Christophe; Coquel, Frédéric; LeFloch, Philippe G. 11 2012 A Godunov-type method for the shallow water equations with discontinuous topography in the resonant regime. Zbl 1453.35150LeFloch, Philippe G.; Thanh, Mai Duc 37 2011 The characteristic initial value problem for plane symmetric spacetimes with weak regularity. Zbl 1222.83028LeFloch, Philippe G.; Stewart, John M. 17 2011 A global foliation of Einstein-Euler spacetimes with Gowdy-symmetry on \(T ^{3}\). Zbl 1256.35165LeFloch, Philippe G.; Rendall, Alan D. 12 2011 Plane-symmetric spacetimes with positive cosmological constant: the case of stiff fluids. Zbl 1247.83012LeFloch, Philippe G.; Tchapnda, Sophonie B. 4 2011 Hyperbolic conservation laws on spacetimes. Zbl 1248.35124LeFloch, Philippe G. 4 2011 Coupling techniques for nonlinear hyperbolic equations. I: Self-similar diffusion for thin interfaces. Zbl 1252.35188Boutin, Benjamin; Coquel, Frédéric; LeFloch, Philippe G. 3 2011 A geometric approach to error estimates for conservation laws posed on a spacetime. Zbl 1221.35229Amorim, Paulo; LeFloch, Philippe G.; Neves, Wladimir 3 2011 Second-order hyperbolic Fuchsian systems and applications. Zbl 1206.83025Beyer, Florian; LeFloch, Philippe G. 10 2010 Kinetic relations for undercompressive shock waves. Physical, mathematical, and numerical issues. Zbl 1221.35235LeFloch, Philippe G. 8 2010 Global geometry of \(T^2\)-symmetric spacetimes with weak regularity. Zbl 1205.83017LeFloch, Philippe G.; Smulevici, Jacques 4 2010 Uniqueness of Kottler spacetime and the Besse conjecture. Zbl 1202.83068LeFloch, Philippe G.; Rozoy, Luc 4 2010 Existence of naked singularities in the Brans-Dicke theory of gravitation. An analytical and numerical study. Zbl 1208.83081Bedjaoui, Nabil; LeFloch, Philippe G.; Martín-García, José M.; Novak, Jérôme 2 2010 Diminishing functionals for nonclassical entropy solutions selected by kinetic relations. Zbl 1207.35219Laforest, Marc; LeFloch, Philippe G. 1 2010 A symmetrization of the relativistic Euler equations with several spatial variables. Zbl 1192.35118LeFloch, Philippe G.; Ukai, Seiji 13 2009 Hyperbolic conservation laws on the sphere. A geometry-compatible finite volume scheme. Zbl 1168.65372Ben-Artzi, Matania; Falcovitz, Joseph; LeFloch, Philippe G. 12 2009 Hyperbolic conservation laws on manifolds. An error estimate for finite volume schemes. Zbl 1178.35251LeFloch, Philippe G.; Okutmustur, Baver; Neves, Wladimir 7 2009 Kinetic functions in magnetohydrodynamics with resistivity and Hall effect. Zbl 1212.35301LeFloch, Philippe G.; Mishra, Siddhartha 3 2009 A kinetic decomposition for singular limits of non-local conservation laws. Zbl 1180.35349Kissling, Frederike; LeFloch, Philippe G.; Rohde, Christian 3 2009 Local foliations and optimal regularity of Einstein spacetimes. Zbl 1179.53069Chen, Bing-Long; LeFloch, Philippe G. 3 2009 Computing Gowdy spacetimes via spectral evolution in future and past directions. Zbl 1158.83301Amorim, Paulo; Bernardi, Christine; LeFloch, Philippe G. 2 2009 Isometric immersions into the Minkowski spacetime for Lorentzian manifolds with limited regularity. Zbl 1161.53063Lefloch, Philippe G.; Mardare, Cristinel; Mardare, Sorin 1 2009 Why many theories of shock waves are necessary: convergence error in formally path-consistent schemes. Zbl 1176.76084Castro, Manuel J.; LeFloch, Philippe G.; Muñoz-Ruiz, María Luz; Parés, Carlos 73 2008 The minimum entropy principle for compressible fluid flows in a nozzle with discontinuous cross-section. Zbl 1139.76048Kröner, Dietmar; LeFloch, Philippe G.; Thanh, Mai-Duc 24 2008 The hyperbolic mean curvature flow. Zbl 1159.53025LeFloch, Philippe G.; Smoczyk, Knut 14 2008 Convergent and conservative schemes for nonclassical solutions based on kinetic relations. I. Zbl 1157.65435Boutin, Benjamin; Chalons, Christophe; Lagoutière, Frédéric; LeFloch, Philippe G. 13 2008 Finite volume schemes on Lorentzian manifolds. Zbl 1179.35027Amorim, Paulo; LeFloch, Philippe G.; Okutmustur, Baver 11 2008 Hyperbolic conservation laws on space-times. A finite volume scheme based on differential forms. Zbl 1178.35250LeFloch, Philippe G.; Okutmustur, Baver 9 2008 Why many theories of shock waves are necessary: Kinetic functions, equivalent equations, and fourth-order models. Zbl 1264.76055LeFloch, Philippe G.; Mohammadian, Majid 9 2008 Injectivity radius of Lorentzian manifolds. Zbl 1156.53040Chen, Bing-Long; LeFloch, Philippe G. 8 2008 Hyperbolic conservation laws and spacetimes with limited regularity. Zbl 1140.35301LeFloch, P. G. 4 2008 Hyperbolic conservation laws on manifolds with limited regularity. Zbl 1145.35428LeFloch, Philippe G.; Okutmustur, Baver 3 2008 Injectivity radius and optimal regularity of Lorentzian manifolds with bounded curvature. Zbl 1191.53052LeFloch, Philippe G. 2 2008 Mini-workshop: Hyperbolic aspects of phase transition dynamics. Abstracts from the mini-workshop held February 24 – March 1, 2008. Zbl 1177.35008Colombo, Rinaldo M. (ed.); Kröner, Dietmar (ed.); LeFloch, Philippe G. (ed.) 1 2008 Coupling two scalar conservation laws via Dafermos’ self-similar regularization. Zbl 1391.35269Ambroso, A.; Boutin, B.; Coquel, F.; Godlewski, E.; LeFloch, P. G. 1 2008 The Riemann problem for the shallow water equations with discontinuous topography. Zbl 1145.35082LeFloch, Philippe G.; Thanh, Mai Duc 43 2007 Finite energy solutions to the isentropic Euler equations with geometric effects. Zbl 1188.35150LeFloch, Philippe G.; Westdickenberg, Michael 24 2007 Well-posedness theory for geometry-compatible hyperbolic conservation laws on manifolds. Zbl 1138.35055Ben-Artzi, Matania; LeFloch, Philippe G. 16 2007 Definition and stability of Lorentzian manifolds with distributional curvature. Zbl 1144.35311LeFloch, Philippe G.; Mardare, Cristinel 15 2007 A version of the Glimm method based on generalized Riemann problems. Zbl 1125.35003Hong, John M.; LeFloch, Philippe G. 13 2007 Singular limits in phase dynamics with physical viscosity and capillarity. Zbl 1134.35073Joseph, K. T.; LeFloch, P. G. 5 2007 Nonlinear hyperbolic systems: Nondegenerate flux, inner speed variation, and graph solutions. Zbl 1124.35040Glass, Olivier; LeFloch, Philippe G. 4 2007 Singular limits for the Riemann problem: general diffusion, relaxation, and boundary conditions. Zbl 1109.65074Joseph, Kayyunnapara T.; LeFloch, Philippe G. 2 2007 Entropy solutions of the Euler equations for isothermal relativistic fluids. Zbl 1153.76067LeFloch, Philippe G.; Yamazaki, Mitsuru 1 2007 Singular limits for the Riemann problem: general diffusion relaxation, and boundary conditions. Zbl 1209.35078Joseph, K. T.; LeFloch, P. G. 6 2006 Uniqueness for multidimensional hyperbolic systems with commuting Jacobians. Zbl 1103.35068Frid, Hermano; LeFloch, Philippe G. 3 2006 Non-monotonic traveling waves in van der Waals fluids. Zbl 1083.35060Bedjaoui, N.; Chalons, C.; Coquel, F.; LeFloch, P. G. 17 2005 Hyperbolic conservation laws on manifolds: total variation estimates and the finite volume method. Zbl 1114.35121Amorim, Paulo; Ben-Artzi, Matania; LeFloch, Philippe G. 13 2005 Symmetries and global solvability of the isothermal gas dynamics equations. Zbl 1178.76302LeFloch, Philippe G.; Shelukhin, Vladimir 7 2005 The Riemann problem for a class of resonant hyperbolic systems of balance laws. Zbl 1086.35069Goatin, Paola; LeFloch, Philippe G. 53 2004 Graph solutions of nonlinear hyperbolic systems. Zbl 1071.35078LeFloch, Philippe G. 14 2004 Diffusive-dispersive travelling waves and kinetic relations. V: Singular diffusion and nonlinear dispersion. Zbl 1065.35182Bedjaoui, Nabil; LeFloch, Philippe G. 14 2004 The Glimm scheme for perfect fluids on plane-symmetric Gowdy spacetimes. Zbl 1080.83011Barnes, A. P.; LeFloch, P. G.; Schmidt, B. G.; Stewart, J. M. 13 2004 Nonclassical Riemann solvers with nucleation. Zbl 1090.35121LeFloch, P. G.; Shearer, M. 6 2004 Continuous Glimm-type functionals and spreading of rarefunction waves. Zbl 1094.35077LeFloch, Phillippe; Trivisa, Konstantina 4 2004 Existence theory for nonclassical entropy solutions of scalar conservation laws. Zbl 1082.35103Baiti, Paolo; LeFloch, Philippe G.; Piccoli, Benedetto 2 2004 On the validity of Chapman-Enskog expansions for shock waves with small strength. Zbl 1071.35080Bedjaoui, Nabil; Klingenberg, Christian; LeFloch, Philippe G. 1 2004 The Riemann problem for fluid flows in a nozzle with discontinuous cross-section. Zbl 1091.35044LeFloch, Philippe G.; Mai Duc Thanh 47 2003 ...and 81 more Documents all cited Publications top 5 cited Publications all top 5 Cited by 1,401 Authors 81 LeFloch, Philippe Gerard 37 Mai Duc Thanh 36 Dumbser, Michael 25 Parés Madroñal, Carlos 23 Coclite, Giuseppe Maria 21 Chalons, Christophe 19 Castro, Manuel J. 19 Toro, Eleuterio F. 18 Rohde, Christian 17 Colombo, Rinaldo M. 17 Di Ruvo, Lorenzo 17 Sarrico, Carlos Orlando R. 17 Shao, Zhiqiang 17 Yang, Hanchun 16 Chen, Gui-Qiang G. 15 Gosse, Laurent 15 Hérard, Jean-Marc 14 Berthon, Christophe 14 Coquel, Frédéric 14 Mishra, Siddhartha 13 Castro-Díaz, Manuel Jesús 13 Goatin, Paola 12 Fernández-Nieto, Enrique Domingo 12 Hong, John Meng-Kai 12 Karlsen, Kenneth Hvistendahl 11 Kröner, Dietmar 11 Mitrovic, Darko 11 Shen, Chun 11 Sun, Meina 10 Corli, Andrea 10 Giesselmann, Jan 10 Seguin, Nicolas 9 Cheng, Hongjun 9 Cuong, Dao Huy 9 Li, Jiequan 9 Risebro, Nils Henrik 9 Rosini, Massimiliano Daniele 9 Wei, Changhua 8 Andreianov, Boris 8 Boscarino, Sebastiano 8 Bouchut, François 8 Després, Bruno 8 Joseph, Kayyunnapara Thomas 8 Morales de Luna, Tomás 8 Piccoli, Benedetto 8 Raviart, Pierre-Arnaud 8 Shu, Chi-Wang 8 Tadmor, Eitan 7 Amadori, Debora 7 Balsara, Dinshaw S. 7 Ben-Artzi, Matania 7 Bürger, Raimund 7 Gassner, Gregor J. 7 Godlewski, Edwige 7 Klingenberg, Christian 7 Lu, Yunguang 7 Murillo, Javier 7 Shearer, Michael 7 Sheng, Wancheng 7 Speck, Jared 7 Yang, Tong 7 Zhao, Huijiang 6 Ancona, Fabio 6 Bressan, Alberto 6 Dias, João-Paulo 6 Dubey, Ritesh Kumar 6 Frid, Hermano 6 Garavello, Mauro 6 Kong, Dexing 6 Ma, Yue 6 Montecinos, Gino I. 6 Müller, Siegfried 6 Rosatti, Giorgio 6 Svärd, Magnus 6 van der Vegt, Jaap J. W. 6 Wang, Zenggui 6 Warnecke, Gerald G. 6 Winters, Andrew R. 5 Abreu, Eduardo 5 Aguillon, Nina 5 Bianchini, Stefano 5 Bokhove, Onno 5 Boscheri, Walter 5 Breuß, Michael 5 Christoforou, Cleopatra C. 5 Cockburn, Bernardo 5 Figueira, Mário S. R. 5 Fjordholm, Ulrik Skre 5 Foucher, Françoise 5 Gallouët, Thierry 5 Garcia-Navarro, Pilar 5 Gowda, G. D. Veerappa 5 Hantke, Maren 5 Hattori, Harumi 5 Helluy, Philippe 5 Hidalgo, Arturo 5 Kalisch, Henrik 5 Kondo, Cezar I. 5 Kunzinger, Michael 5 Lagoutière, Frédéric ...and 1,301 more Authors all top 5 Cited in 213 Serials 142 Journal of Computational Physics 81 Journal of Differential Equations 63 Journal of Hyperbolic Differential Equations 51 Computers and Fluids 42 Journal of Mathematical Analysis and Applications 42 Journal of Scientific Computing 40 Mathematics of Computation 30 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods 28 Archive for Rational Mechanics and Analysis 25 ZAMP. 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