World's Best Scientists 2026 revealed!
Raphaèle Herbin

Raphaèle Herbin

D-Index & Metrics

Mathematics

D-Index
45
Citations
9823
World Ranking
1452
National Ranking
83

Engineering and Technology

D-Index
45
Citations
9761
World Ranking
5386
National Ranking
109

Overview

Raphaèle Herbin is affiliated with Aix-Marseille University in France. Their research spans the fields of Engineering and Mathematics, with notable emphasis on Computational Mechanics and Applied Mathematics. This scientist has contributed extensively to Computational Fluid Dynamics and Aerodynamics, Advanced Numerical Methods in Computational Mathematics, and Gas Dynamics and Kinetic Theory, among other topics.

Herbin's recent scholarly work demonstrates a focus on numerical schemes and finite volume methods applied to fluid dynamics and compressible flow problems. Notable publications include:

  • Low Mach number limit of some staggered schemes for compressible barotropic flows (2020), Mathematics of Computation
  • Conservativity and weak consistency of a class of staggered finite volume methods for the Euler equations (2020), Mathematics of Computation
  • Lax-Wendroff consistency of finite volume schemes for systems of nonlinear conservation laws: extension to staggered schemes (2021), SeMA Journal

Alongside these, other relevant works from collaborators and coauthors include:

  • A Staggered Scheme for the Compressible Euler Equations on General 3D Meshes (2024), Journal of Scientific Computing
  • Optimal error bounds for the two-point flux approximation finite volume scheme (2024), Mathematics of Computation

Frequent collaborators in Herbin's research encompass Thierry Gallouët, J.-C. Latché, Jean-Claude Latché, Youssouf Nasseri, and Aubin Brunel. This reflects a consistent team effort in advancing numerical methods for fluid dynamics and computational mathematics.

Herbin's work appears regularly in several scientific publication venues, with a concentration of papers in:

  • arXiv (Cornell University)
  • Mathematics of Computation
  • SeMA Journal
  • International Journal for Numerical Methods in Fluids
  • Journal of Scientific Computing

The scientist is also preparing a book with Springer Nature titled Weak Solutions of Partial Differential Equations, expected in 2025.

Their scholarly contributions center primarily on computational methods applied to partial differential equations arising in fluid dynamics, gas dynamics, and the numerical approximation of conservation laws. Main topics covered include:

  • Computational Fluid Dynamics and Aerodynamics
  • Advanced Numerical Methods in Computational Mathematics
  • Gas Dynamics and Kinetic Theory
  • Navier-Stokes equation solutions
  • Combustion and Detonation Processes
  • Differential Equations and Numerical Methods
  • Fluid Dynamics and Turbulent Flows

Best Publications

  • Finite Volume Methods

    Robert Eymard;Thierry Gallouët;Raphaèle Herbin

  • Three-dimensional numerical simulation for various geometries of solid oxide fuel cells

    J.R. Ferguson;J.M. Fiard;R. Herbin

  • Discretization of heterogeneous and anisotropic diffusion problems on general nonconforming meshes SUSHI: a scheme using stabilization and hybrid interfaces

    Robert Eymard;Thierry Gallouët;Raphaele Herbin

  • 3D Benchmark on Discretization Schemes for Anisotropic Diffusion Problems on General Grids

    Robert Eymard;Gérard Henry;Raphaèle Herbin;Florence Hubert

  • A UNIFIED APPROACH TO MIMETIC FINITE DIFFERENCE, HYBRID FINITE VOLUME AND MIXED FINITE VOLUME METHODS

    Jerome Droniou;Robert Eymard;Thierry Gallouet;Raphaele Herbin

  • Convergence of a finite volume scheme for nonlinear degenerate parabolic equations

    Robert Eymard;Thierry Gallouët;Raphaèle Herbin;Anthony Michel

  • Small-stencil 3D schemes for diffusive flows in porous media

    Robert Eymard;Cindy Guichard;Raphaele Herbin

  • Error estimates for the approximate solutions of a nonlinear hyperbolic equation given by finite volume schemes

    R Eymard;T Gallouët;M Ghilani;R Herbin

  • Benchmark on Discretization Schemes for Anisotropic Diffusion Problems on General Grids

    Raphaele Herbin;Florence Hubert

  • An error estimate for a finite volume scheme for a diffusion–convection problem on a triangular mesh

    Raphaèle Herbin

  • A cell-centred finite-volume approximation for anisotropic diffusion operators on unstructured meshes in any space dimension

    Robert Eymard;Thierry Gallouët;Raphaèle Herbin

  • GRADIENT SCHEMES: A GENERIC FRAMEWORK FOR THE DISCRETISATION OF LINEAR, NONLINEAR AND NONLOCAL ELLIPTIC AND PARABOLIC EQUATIONS

    Jerome Droniou;Robert Eymard;Thierry Gallouet;Raphaele Herbin

  • Mathematical study of a petroleum-engineering scheme

    Robert Eymard;Raphaèle Herbin;Anthony Michel

  • The Gradient Discretisation Method

    Jérôme Droniou;Robert Eymard;Thierry Gallouët;Cindy Guichard

  • Error Estimates on the Approximate Finite Volume Solution of Convection Diffusion Equations with General Boundary Conditions

    Thierry Gallouët;Raphaèle Herbin;Marie Hélène Vignal

  • AN UNCONDITIONALLY STABLE PRESSURE CORRECTION SCHEME FOR THE COMPRESSIBLE BAROTROPIC NAVIER-STOKES EQUATIONS

    Thierry Gallouët;Laura Gastaldo;Raphaele Herbin;Jean-Claude Latché

  • EXISTENCE AND UNIQUENESS OF THE ENTROPY SOLUTION TO A NONLINEAR HYPERBOLIC EQUATION

    R.Eymard;T.Gallouёt;R.Herbin

  • A new finite volume scheme for anisotropic diffusion problems on general grids: convergence analysis

    Robert Eymard;Thierry Gallouët;Raphaèle Herbin

  • Vertex-centred discretization of multiphase compositional Darcy flows on general meshes

    Robert Eymard;Cindy Guichard;Raphaele Herbin;Roland Masson

  • Finite volume approximation of elliptic problems and convergence of an approximate gradient

    R. Eymard;T. Gallouët;R. Herbin

  • Finite volume method

    Robert Eymard;Herbin;Thierry Gallouët

  • Discretisation of heterogeneous and anisotropic diffusion problems on general non-conforming meshes. SUSHI: a scheme using stabilisation and hybrid interfaces

    Robert Eymard;Thierry Gallouët;Raphaele Herbin

Frequent Co-Authors

Thierry Gallouët
Thierry Gallouët Aix-Marseille University
Robert Eymard
Robert Eymard University of Paris-Est
Jérôme Droniou
Jérôme Droniou University of Montpellier
Neil R. Baker
Neil R. Baker University of Essex
Tracy Lawson
Tracy Lawson University of Illinois at Urbana-Champaign
Gabriel Cornic
Gabriel Cornic University of Paris-Saclay
Ludovic Leclercq
Ludovic Leclercq Université Gustave Eiffel
Gianmarco Manzini
Gianmarco Manzini Los Alamos National Laboratory

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