An Introduction to Nonclassical Shocks of Systems of Conservation Laws. - Philippe G. LeFloch (Theory and Numerics for Conservation Laws, 1997)

Generalized monotone schemes, discrete paths of extrema, and discrete entropy conditions. - Philippe G. LeFloch; Jian-Guo Liu (Math. Comput., 1999)

Nonclassical Shocks and Kinetic Relations: Strictly Hyperbolic Systems. - Brian T. Hayes; Philippe G. LeFloch (SIAM J. Math. Anal., 2000)

High-Order Schemes, Entropy Inequalities, and Nonclassical Shocks. - Philippe G. LeFloch; Christian Rohde (SIAM J. Numer. Anal., 2000)

A fully discrete scheme for diffusive-dispersive conservation laws. - Christophe Chalons; Philippe G. LeFloch (Numerische Mathematik, 2001)

Zero Diffusion-Dispersion Limits for Scalar Conservation Laws. - Cezar I. Kondo; Philippe G. LeFloch (SIAM J. Math. Anal., 2002)

Fully Discrete, Entropy Conservative Schemes of ArbitraryOrder. - Philippe G. LeFloch; J. M. Mercier; Christian Rohde (SIAM J. Numer. Anal., 2002)

Why many theories of shock waves are necessary: Convergence error in formally path-consistent schemes. - Manuel J. Castro; Philippe G. LeFloch; María Luz Muñoz-Ruiz; Carlos Parés (J. Comput. Phys., 2008)

Why many theories of shock waves are necessary: Kinetic functions, equivalent equations, and fourth-order models. - Philippe G. LeFloch; Majid Mohammadian (J. Comput. Phys., 2008)

Leaf superposition property for integer rectifiable currents. - Luigi Ambrosio; Gianluca Crippa; Philippe G. LeFloch (Networks Heterog. Media, 2008)

Hyperbolic conservation laws on the sphere. A geometry-compatible finite volume scheme. - Matania Ben-Artzi; Joseph Falcovitz; Philippe G. LeFloch (J. Comput. Phys., 2009)

A Godunov-type method for the shallow water equations with discontinuous topography in the resonant regime. - Philippe G. LeFloch; Mai Duc Thanh (J. Comput. Phys., 2011)

Relativistic Burgers Equations on Curved Spacetimes. Derivation and Finite Volume Approximation. - Philippe G. LeFloch; Hasan Makhlof; Baver Okutmustur (SIAM J. Numer. Anal., 2012)

Late-time/stiff-relaxation asymptotic-preserving approximations of hyperbolic equations. - Christophe Berthon; Philippe G. LeFloch; Rodolphe Turpault (Math. Comput., 2013)

Coupling Techniques for Nonlinear Hyperbolic Equations. III. The Well-Balanced Approximation of Thick Interfaces. - Benjamin Boutin; Frédéric Coquel; Philippe G. LeFloch (SIAM J. Numer. Anal., 2013)

Numerical methods with controlled dissipation for small-scale dependent shocks. - Philippe G. LeFloch; Siddhartha Mishra (Acta Numer., 2014)

High-Order Asymptotic-Preserving Methods for Fully Nonlinear Relaxation Problems. - Sebastiano Boscarino; Philippe G. LeFloch; Giovanni Russo 001 (SIAM J. Sci. Comput., 2014)

The Hyperboloidal Foliation Method - Philippe G. LeFloch; Yue Ma (World Scientific, 2015)

Revisiting the method of characteristics via a convex hull algorithm. - Philippe G. LeFloch; Jean-Marc Mercier (J. Comput. Phys., 2015)

Coupling techniques for nonlinear hyperbolic equations. IV. Well-balanced schemes for scalar multi-dimensional and multi-component laws. - Benjamin Boutin; Frédéric Coquel; Philippe G. LeFloch (Math. Comput., 2015)

On the Area of the Symmetry Orbits in Weakly Regular Einstein-Euler Spacetimes with Gowdy Symmetry. - Nastasia Grubic; Philippe G. LeFloch (SIAM J. Math. Anal., 2015)

Schemes with Well-Controlled Dissipation. - Jan Ernest; Philippe G. LeFloch; Siddhartha Mishra (SIAM J. Numer. Anal., 2015)

Nonlocal Conservation Laws. A New Class of Monotonicity-Preserving Models. - Qiang Du 001; Zhan Huang; Philippe G. LeFloch (SIAM J. Numer. Anal., 2017)

Mesh-free error integration in arbitrary dimensions: a numerical study of discrepancy functions. - Philippe G. LeFloch; Jean-Marc Mercier (CoRR, 2019)

The Transport-based Mesh-free Method (TMM) and its applications in finance: a review. - Philippe G. LeFloch; Jean-Marc Mercier (CoRR, 2019)

Asymptotic structure of cosmological Burgers flows in one and two space dimensions: a numerical study. - Yangyang Cao; Mohammad A. Ghazizadeh; Philippe G. LeFloch (CoRR, 2019)

Augmented hyperbolic models with diffusive-dispersive shocks. - Philippe G. LeFloch; Allen M. Tesdall (CoRR, 2019)

Asymptotic structure of cosmological fluid flows in one and two space dimensions: a numerical study. - Yangyang Cao; Mohammad A. Ghazizadeh; Philippe G. LeFloch (CoRR, 2019)

Well-balanced algorithms for relativistic fluids on a Schwarzschild background. - Philippe G. LeFloch; Carlos Parés; Ernesto Pimentel-García (CoRR, 2020)

A well-balanced positivity preserving cell-vertex finite volume method satisfying the discrete maximum-minimum principle for coupled models of surface water flow and scalar transport. - Hasan Karjoun; Abdelaziz Beljadid; Philippe G. LeFloch (CoRR, 2020)

Formulation and convergence of the finite volume method for conservation laws on spacetimes with boundary. - Jan Giesselmann; Philippe G. LeFloch (Numerische Mathematik, 2020)

A numerical algorithm for Fuchsian equations and fluid flows on cosmological spacetimes. - Florian Beyer 001; Philippe G. LeFloch (J. Comput. Phys., 2021)

A Class of Well-Balanced Algorithms for Relativistic Fluids on a Schwarzschild Background. - Philippe G. LeFloch; Carlos Parés; Ernesto Pimentel-García (J. Sci. Comput., 2021)

Kinetic Functions for Nonclassical Shocks, Entropy Stability, and Discrete Summation by Parts. - Philippe G. LeFloch; Hendrik Ranocha (J. Sci. Comput., 2021)

Coupling techniques for nonlinear hyperbolic equations. Ⅱ. resonant interfaces with internal structure. - Benjamin Boutin; Frédéric Coquel; Philippe G. LeFloch (Networks Heterog. Media, 2021)

A structure-preserving algorithm for surface water flows with transport processes. - Hasan Karjoun; Abdelaziz Beljadid; Philippe G. LeFloch (Adv. Comput. Math., 2022)

A Class of Mesh-Free Algorithms for Some Problems Arising in Finance and Machine Learning. - Philippe G. LeFloch; Jean-Marc Mercier (J. Sci. Comput., 2023)

CodPy: a Python library for numerics, machine learning, and statistics. - Philippe G. LeFloch; Jean-Marc Mercier; Shohruh Miryusupov (CoRR, 2024)

Extrapolation and generative algorithms for three applications in finance. - Philippe G. LeFloch; Jean-Marc Mercier; Shohruh Miryusupov (CoRR, 2024)

A class of kernel-based scalable algorithms for data science. - Philippe G. LeFloch; Jean-Marc Mercier; Shohruh Miryusupov (CoRR, 2024)