Raphaèle Herbin

Q: What Schools Are Affiliated With Raphaèle Herbin

Raphaèle Herbin is affiliated with the following schools: University of Essex, Claude Bernard University Lyon 1, Aix-Marseille University

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Raphaèle Herbin

Mathematics

#2848

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#4312

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Algebraic Geometry

#179

World Rank

#187

Historical Rank

Measure Theory

#2932

World Rank

#3481

Historical Rank

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Mathematics

Why Is Raphaèle Herbin Influential?

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According to Wikipedia, Raphaèle Herbin is a French applied mathematician; she is known for her work on the finite volume method. Herbin has been a professor at Aix-Marseille University since 1995, and directs the Institut de Mathématiques de Marseille. She earned her doctorate in 1986 at Claude Bernard University Lyon 1, with the dissertation Approximation numérique d'inéquations variationnelles non linéaires par des méthodes de continuation supervised by Francis Conrad.

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Raphaèle Herbin's Published Works

Number of citations in a given year to any of this author's works

Total number of citations to an author for the works they published in a given year. This highlights publication of the most important work(s) by the author

Published Works

Finite volume methods (2000) (1124)
Three-dimensional numerical simulation for various geometries of solid oxide fuel cells (1996) (420)
Discretization of heterogeneous and anisotropic diffusion problems on general nonconforming meshes SUSHI: a scheme using stabilization and hybrid interfaces (2008) (356)
3D Benchmark on Discretization Schemes for Anisotropic Diffusion Problems on General Grids (2008) (297)
A UNIFIED APPROACH TO MIMETIC FINITE DIFFERENCE, HYBRID FINITE VOLUME AND MIXED FINITE VOLUME METHODS (2008) (243)
Finite volume method (2010) (211)
Convergence of a finite volume scheme for nonlinear degenerate parabolic equations (2002) (206)
Small-stencil 3D schemes for diffusive flows in porous media (2012) (160)
An error estimate for a finite volume scheme for a diffusion–convection problem on a triangular mesh (1995) (145)
GRADIENT SCHEMES: A GENERIC FRAMEWORK FOR THE DISCRETISATION OF LINEAR, NONLINEAR AND NONLOCAL ELLIPTIC AND PARABOLIC EQUATIONS (2013) (141)
Error estimates for the approximate solutions of a nonlinear hyperbolic equation given by finite volume schemes (1998) (140)
The Gradient Discretisation Method (2018) (139)
A cell-centred finite-volume approximation for anisotropic diffusion operators on unstructured meshes in any space dimension (2006) (123)
Mathematical study of a petroleum-engineering scheme (2003) (111)
Error Estimates on the Approximate Finite Volume Solution of Convection Diffusion Equations with General Boundary Conditions (2000) (93)
AN UNCONDITIONALLY STABLE PRESSURE CORRECTION SCHEME FOR THE COMPRESSIBLE BAROTROPIC NAVIER-STOKES EQUATIONS (2008) (86)
Finite volume approximation of elliptic problems and convergence of an approximate gradient (2001) (81)
Convergence of finite volume schemes for semilinear convection diffusion equations (1999) (79)
Vertex-centred discretization of multiphase compositional Darcy flows on general meshes (2012) (78)
A new finite volume scheme for anisotropic diffusion problems on general grids: convergence analysis (2007) (77)
Lateral Diffusion of CO2 in Leaves Is Not Sufficient to Support Photosynthesis[w] (2005) (75)
EXISTENCE AND UNIQUENESS OF THE ENTROPY SOLUTION TO A NONLINEAR HYPERBOLIC EQUATION (1995) (75)
Gradient schemes for two‐phase flow in heterogeneous porous media and Richards equation (2014) (73)
A nine point finite volume scheme for the simulation of diffusion in heterogeneous media (2009) (70)
Existence of a solution to a coupled elliptic system with a Signorini condition (1994) (68)
Gradient schemes: Generic tools for the numerical analysis of diffusion equations (2015) (65)
A convergent finite element-finite volume scheme for the compressible Stokes problem. Part I: The isothermal case (2007) (63)
A convergent finite element-finite volume scheme for the compressible Stokes problem. Part II: the isentropic case (2009) (59)
On some implicit and semi-implicit staggered schemes for the shallow water and Euler equations (2014) (57)
Discrete Sobolev inequalities and Lp error estimates for finite volume solutions of convection diffusion equations (2001) (57)
Finite Volumes for Complex Applications VI Problems & Perspectives (2011) (56)
Convergence of an upstream finite volume scheme for a nonlinear hyperbolic equation on a triangular mesh (1993) (51)
Error estimates for a numerical approximation to the compressible barotropic Navier-Stokes equations (2015) (49)
VERTEX CENTRED DISCRETIZATION OF TWO-PHASE DARCY FLOWS ON GENERAL MESHES (2012) (47)
Gradient schemes for the Stefan problem (2013) (47)
A Finite Volume Scheme for a Noncoercive Elliptic Equation with Measure Data (2003) (43)
On a stabilized colocated finite volume scheme for the Stokes problem submitted to M2AN (2006) (40)
Convergence of the MAC Scheme for the Compressible Stokes Equations (2010) (39)
An unconditionally stable staggered pressure correction scheme for the compressible Navier-Stokes equations (2016) (39)
A finite volume scheme for anisotropic diffusion problems (2004) (36)
Comparison between finite volume and finite element methods for an elliptic system arising in electrochemical engineering (1994) (34)
EXPLICIT STAGGERED SCHEMES FOR THE COMPRESSIBLE EULER EQUATIONS (2013) (34)
Error estimate for approximate solutions of a nonlinear convection-diffusion problem (2002) (34)
Staggered discretizations, pressure correction schemes and all speed barotropic flows (2011) (33)
Diffusion with dissolution and precipitation in a porous medium: Mathematical analysis and numerical approximation of a simplified model (2007) (29)
Cell centred discretisation of non linear elliptic problems on general multidimensional polyhedral grids (2009) (29)
Kinetic energy control in the MAC discretization of compressible Navier-Stokes equations (2010) (28)
APPROXIMATION BY THE FINITE VOLUME METHOD OF AN ELLIPTIC-PARABOLIC EQUATION ARISING IN ENVIRONMENTAL STUDIES (2001) (28)
Finite volume approximation of a class of variational inequalities (2001) (27)
Finite volume schemes for the biharmonic problem on general meshes (2012) (27)
A new colocated finite volume scheme for the incompressible Navier-Stokes equations on general non matching grids (2007) (27)
Discretization of coupled heat and electrical diffusion problems by finite-element and finite-volume methods (2007) (25)
STAGGERED SCHEMES FOR ALL SPEED FLOWS (2012) (25)
The Lions domain decomposition algorithm on non‐matching cell‐centred finite volume meshes (2004) (25)
A staggered finite volume scheme on general meshes for the Navier-Stokes equations in two space dimensions (2005) (24)
A discretization of the phase mass balance in fractional step algorithms for the drift-flux model (2011) (24)
Convergence of the Marker-and-Cell Scheme for the Incompressible Navier–Stokes Equations on Non-uniform Grids (2018) (24)
Consistent segregated staggered schemes with explicit steps for the isentropic and full Euler equations (2018) (23)
Pressure correction staggered schemes for barotropic one-phase and two-phase flows (2013) (23)
An error estimate for finite volume methods for the Stokes equations on equilateral triangular meshes (2004) (23)
An extension of the MAC scheme to locally refined meshes: convergence analysis for the full tensor time-dependent Navier–Stokes equations (2015) (23)
Analysis tools for finite volume schemes (2007) (22)
W1,q stability of the Fortin operator for the MAC scheme (2012) (22)
The nite volume method (2000) (21)
Finite volume schemes for elliptic and elliptic-hyperbolic problems on triangular meshes (1997) (20)
A staggered finite volume scheme on general meshes for the generalized Stokes problem in two space dimensions AstaggeredschemefortheStokesequations (2005) (20)
A formally second‐order cell centred scheme for convection–diffusion equations on general grids (2013) (19)
Gradient Scheme Approximations for Diffusion Problems (2011) (19)
Finite volume methods Hand-book of Numerical Analysis (2000) (18)
An unconditionnally stable pressure correction scheme for compressible barotropic Navier-Stokes equations (2007) (18)
A collocated finite volume scheme to solve free convection for general non-conforming grids (2008) (17)
A cell-centered finite volume scheme on general meshes for the Stokes equations in two space dimensions (2003) (16)
Approximation of Obstacle Problems by Continuation Methods (1988) (16)
Benchmark 3D: the VAG scheme (2011) (16)
Convergence analysis of a locally stabilized collocated finite volume scheme for incompressible flows (2009) (15)
An unconditionally stable finite element-finite volume pressure correction scheme for the drift-flux model (2010) (15)
A uniqueness result for measure-valued solutions of nonlinear hyperbolic equations (1993) (14)
Convergence of linear finite elements for diffusion equations with measure data (2004) (14)
Discontinuous Galerkin Discretization and hp-Refinement for the Resolution of the Neutron Transport Equation (2013) (14)
A cell-centred finite volume approximation for second order partial derivative operators with full matrix on unstructured meshes in any space dimension (2005) (14)
Instantaneous and noninstantaneous dissolution: approximation by the finite volume method (1999) (13)
SMALL-STENCIL 3 D SCHEMES FOR DIFFUSIVE FLOWS IN POROUS MEDIA (2011) (13)
On the weak consistency of finite volumes schemes for conservation laws on general meshes (2019) (13)
Convergence of the MAC scheme for the compressible stationary Navier-Stokes equations (2016) (12)
Conservativity And Weak Consistency Of A Class Of Staggered Finite Volume Methods For The Euler Equations (2019) (12)
A MUSCL-type segregated – explicit staggered scheme for the Euler equations (2018) (12)
Convergence of the MAC Scheme for the Steady-State Incompressible Navier-Stokes Equations on Non-uniform Grids (2014) (12)
On the stability of colocated clustered finite volume simplicial discretizations for the 2D Stokes problem (2007) (12)
Kinetic energy control in explicit Finite Volume discretizations of the incompressible and compressible Navier-Stokes equations (2010) (12)
CONSISTENT SEMI-IMPLICIT STAGGERED SCHEMES FOR COMPRESSIBLE FLOWS PART I: THE BAROTROPIC EULER EQUATIONS. (2012) (11)
Development of numerical methods for the reactive transport of chemical species in a porous media : a nonlinear conjugate gradient method (2005) (10)
Convergence of the MAC scheme for the incompressible Navier-Stokes equations with variable density and viscosity (2017) (10)
Combined triangular FV‐triangular FE method for nonlinear convection‐diffusion problems (2007) (10)
Collocated finite volume schemes for the simulation of natural convective flows on unstructured meshes (2008) (10)
Applications of approximate gradient schemes for nonlinear parabolic equations (2015) (9)
MESURE, INTEGRATION, PROBABILITES (2013) (9)
Discrete Sobolev Inequalities and L p Error Estimates for Approximate Finite Volume Solutions of Con (1998) (9)
Approximation of the biharmonic problem using P1 finite elements (2011) (8)
A finite volume for anisotropic diffusion problems (2004) (7)
Convergence of the marker-and-cell scheme for the semi-stationary compressible Stokes problem (2017) (7)
Gradient Schemes for Image Processing (2011) (7)
RTk mixed finite elements for some nonlinear problems (2015) (7)
Multiphase Flow in Porous Media Using the VAG Scheme (2011) (7)
Discretization schemes for heterogeneous and anisotropic diffusion problems on general nonconforming meshes (2008) (7)
Axisymmetric finite volumes for the numerical simulation of bulk CO 2 transport and assimilation in a leaf (2005) (7)
Analysis of a fractional-step scheme for the P$$_1$$1 radiative diffusion model (2016) (7)
Discretization of the viscous dissipation term with the MAC scheme (2011) (7)
Lax–Wendroff consistency of finite volume schemes for systems of non linear conservation laws: extension to staggered schemes (2021) (7)
AN UNCONDITIONALLY STABLE PRESSURE CORRECTION SCHEME FOR BAROTROPIC COMPRESSIBLE NAVIER-STOKES EQUATIONS (2006) (6)
On the Discretization of the Coupled Heat and Electrical Diffusion Problems (2006) (6)
An error estimate for a finite volume scheme for a nonlinear hyperbolic equation on a triangular mes (1998) (6)
CONSISTENT SEMI-IMPLICIT STAGGERED SCHEMES FOR COMPRESSIBLE FLOWS PART II: EULER EQUATIONS. (2012) (6)
A fast precipitation and dissolution reaction for a reaction–diffusion system arising in a porous medium☆ (2009) (6)
Consistent explicit staggered schemes for compressible flows Part II: the Euler equation (2013) (6)
A cell-centred pressure-correction scheme for the compressible Euler equations (2020) (5)
Parallel implementation of a multigrid method on the experimental 1CAP supercomputer (1988) (5)
On colocated clustered finite volume schemes for incompressible flow problems (2007) (5)
"A Note on the Entropy Solutions of the Hydrodynamic Model of Traffic Flow" Revisited (2011) (5)
An error estimate for the approximation of linear parabolic equations by the gradient discretization method (2017) (5)
AN ENTROPY PRESERVING FINITE-ELEMENT/FINITE-VOLUME PRESSURE CORRECTION SCHEME FOR THE DRIFT-FLUX MODEL (2008) (5)
Parallel Multilevel Finite Element Method with Hierarchical Basis Functions (1987) (5)
Non-conforming finite elements on polytopal meshes (2020) (4)
Consistent Internal Energy Based Schemes for the Compressible Euler Equations (2019) (4)
Implicit MAC scheme for compressible Navier-Stokes equations: Unconditional error estimates (2017) (4)
Implicit MAC scheme for compressible Navier–Stokes equations: low Mach asymptotic error estimates (2020) (4)
An Extension of the MAC Scheme to some Unstructured Meshes (2011) (4)
Low Mach Number Limit of a Pressure Correction MAC Scheme for Compressible Barotropic Flows (2017) (4)
Approximation of the biharmonic problem using piecewise linear finite elements (2010) (4)
A second order cell centered scheme for convection-diﬀusion equations on unstructured non–conforming grids (2011) (3)
An Introduction to the Gradient Discretisation Method (2017) (3)
Convergence of a finite volume scheme for the biharmonic problem (2010) (3)
A Monotonic Method for the Numerical Solution of Some Free Boundary Value Problems (2002) (3)
Entropy estimates for a class of schemes for the euler equations (2017) (3)
Finite volume schemes and Lax-Wendroff consistency (2021) (3)
The Gradient Discretisation Method for Linear Advection Problems (2019) (3)
Analysis of cell centred finite volume methods for incompressible fluid flows (2006) (3)
A decoupled staggered scheme for the shallow water equations (2019) (2)
A KINETIC ENERGY PRESERVING CONVECTION OPERATOR FOR THE MAC DISCRETIZATION OF COMPRESSIBLE NAVIER-STOKES EQUATIONS (1999) (2)
Error Estimate for the Finite Volume Approximate of the Solution to a Nonlinear Convective Equation (1998) (2)
Upwind Finite Volume Schemes for One and Two Dimensional Euler Equations (2003) (2)
FINITE VOLUME SCHEMES FOR NONLINEAR PARABOLIC PROBLEMS: ANOTHER REGULARIZATION METHOD (2005) (2)
A 3-dimensional planar SOFC stack model (2)
Weak Consistency of Finite Volume Schemes for Systems of Non Linear Conservation Laws: Extension to Staggered Schemes (2021) (2)
Analysis Tools for Gradient Discretisations (2018) (2)
A staggered scheme for the compressible Euler equations on general 3D meshes (2022) (1)
Playing with Burgers’s Equation (2011) (1)
A new unstructured algorithm based on the Volume of Fluid method for tracking material interfaces in a finite-volume framework (2005) (1)
On the effective resistance of an electrolytic membrane (1994) (1)
Modelling of a spherical deflagration at constant speed (2020) (1)
Implementation of a Parallel Multigrid Method on a Loosely Coupled Array of Processors (1987) (1)
Schéma De Volumes Finis en Interaction Fluide/Structure: Faisabilité et Application L'écoulement Vasculaire (1995) (1)
Convergence of the mac scheme for variable density flows (2017) (1)
Existence and uniqueness of the entropy solutionto a nonlinear hyperbolic (1995) (1)
Benchmark 3D: the SUSHI Scheme (2011) (1)
A Consistent Quasi-Second Order Staggered Scheme for the Two-Dimensional Shallow Water Equations (2021) (1)
Convergence of the fully discrete incremental projection scheme for incompressible flows (2022) (1)
Nodal Mimetic Finite Difference Methods (2018) (0)
Neumann, Fourier and Mixed Boundary Conditions (2018) (0)
Will be set by the publisher STAGGERED SCHEMES FOR ALL SPEED FLOWS (2011) (0)
Dirichlet Boundary Conditions (2018) (0)
On the weak consistency of finite volumes schemes for conservation laws on general meshes (2019) (0)
Convergence of the implicit MAC-discretized Navier-Stokes equations with variable density and viscosity on non-uniform grids (2021) (0)
A staggered pressure correction numerical scheme to compute a travelling reactive interface in a partially premixed mixture (2019) (0)
Error Estimates on the Approximate Nite Volume Solution of Convection Diiusion Equations with Dirichlet, Neumann or Robin Boundary Conditions (2000) (0)
A MUSCL-like finite volumes approximation of the momentum convection operator for low-order nonconforming face-centred discretizations (2023) (0)
UPWIND FINITE VOLUME SCHEMES FOR ONE ANDTWO DIMENSIONAL EULER (2006) (0)
Degenerate Parabolic Problems (2018) (0)
Lax–Wendroff consistency of finite volume schemes for systems of non linear conservation laws: extension to staggered schemes (2021) (0)
A Unified Analysis of Elliptic Problems with Various Boundary Conditions and Their Approximation (2018) (0)
Results with a Locally Refined MAC-Like Scheme—Benchmark Session (2017) (0)
The simulation of the transport of contaminants in groundwater flow: error estimates for a finite volume scheme (2000) (0)
on General Meshes (2012) (0)
MUSCL Discretization for the Fluid Flow Convection Operator on Staggered Meshes (2020) (0)
TWO MODELS FOR THE COMPUTATION OF LAMINAR FLAMES IN DUST CLOUDS (2017) (0)
Discontinuous Galerkin Methods (2018) (0)
The Multi-point Flux Approximation MPFA-O Scheme (2018) (0)
Parallel Implementation of a Method on the Experimental * * G-\ (1988) (0)
Time-Dependent GDM (2018) (0)
Applications of approximate gradient schemes for nonlinear parabolic equations (2015) (0)
Three-dimensional numerical simulationfor various geometriesof solid oxide fuel (2007) (0)
Non-conforming Finite Element Methods (2018) (0)
Hybrid Mimetic Mixed Schemes (2018) (0)
Chemistry-Transport coupling : Implicit schemes keeping a code coupling approach (2006) (0)
A Unified Analysis of Elliptic Problems with Various Boundary Conditions and Their Approximation (2019) (0)
A Class of Staggered Schemes for the Compressible Euler Equations (2018) (0)
Nonmatching finite volume grids and the nonoverlapping Schwarz algorithm (0)
Anti‐diffusive alternate‐directions schemes for the transport of step functions (2022) (0)
Towards a generalization of the MAC scheme on unstructured meshes (2009) (0)
$$H_{\mathrm{div}}$$ Conforming GDs from Mixed Finite Element Methods (2018) (0)
Non mat hing nite volume grids and the nonoverlapping S hwarz algorithm (2001) (0)
Modelling CO 2 diffusion and assimilation in a leaf with axisymmetric finite volumes (2005) (0)
Diffusion with dissolution and precipitation in a porous media approximation by a finite volume scheme (2005) (0)
Convergence of the implicit MAC scheme of the incompressible Navier-Stokes equations with variable density and viscosity (2021) (0)
An extension of the MAC scheme to locally refined meshes: convergence analysis for the full tensor time-dependent Navier–Stokes equations (2014) (0)
A Class of Collocated Finite Volume Schemes for Incompressible Flow Problems (2020) (0)
Non Degenerate Parabolic Problems (2018) (0)
Motivation and Basic Ideas (2018) (0)
Convergence of the Marker-and-Cell Scheme for the Incompressible Navier–Stokes Equations on Non-uniform Grids (2016) (0)

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Published Works

Other Resources About Raphaèle Herbin

What Schools Are Affiliated With Raphaèle Herbin?

Raphaèle Herbin's AcademicInfluence.com Rankings