Laboratoire d'Analyse et de Mathématiques Appliquées

UFR de mathématiques

Université Gustave Eiffel

Une introduction à la relativité restreinte, par Georges EYMARD (1921-1998) permet de comprendre la construction de cette théorie à partir des connaissances élémentaires acquises au lycée.

An introduction to special relativity (in French), by Georges EYMARD (1921-1998) proposes a pedagogical construction of the theory from elementary calculations.

The finite volume method:

[1] R. Eymard, T. Gallouët, and R. Herbin.
The finite volume method.
Handbook of Numerical Analysis, Ph. Ciarlet J.L. Lions eds, 7:715–1022, 2000.

The gradient discretisation method:

[2] J. Droniou, R. Eymard, T. Gallouët, C. Guichard, and R. Herbin.
The gradient discretisation method .
Mathématiques et Applications 82. Springer, 2018.

Publications récentes - recent publications

[3] W. Arendt, I. Chalendar, and R. Eymard.
Galerkin approximation of linear problems in Banach and Hilbert spaces.
accepted in IMA Journal of Numerical Analysis, 2020.

[4] J. Droniou and R. Eymard.
High-order mass–lumped schemes for nonlinear degenerate elliptic equations.
SIAM Journal on Numerical Analysis, 58(1):153–188, 2020.

[5] J. Droniou, R. Eymard, T. Gallouët, and R. Herbin.
A unified analysis of elliptic problems with various boundary conditions and their approximation.
Czechoslovak Mathematical Journal, 70:339–368, 2020.

[6] J. Droniou, R. Eymard, T. Gallouët, and R. Herbin.
The Gradient Discretisation Method for Linear Advection Problems.
Computational Methods in Applied Mathematics,, 20(3):437–458, 2020.

[7] R. Eymard, C. Guichard, and X. Lhébrard.
Convergence of numerical schemes for a conservation equation with convection and degenerate diffusion.
accepted in Journal of Computational Mathematics, 2020.

[8] J. Droniou, R. Eymard, A. Prignet, and K. S. Talbot.
Unified convergence analysis of numerical schemes for a miscible displacement problem.
Foundations of Computational Mathematics, 19(2):333–374, Apr 2019.

[9] S. Phongthanapanich and R. Eymard.
A Comparative Study of Characteristic Finite Element and Characteristic Finite Volume Methods for Convection-Diffusion-Reaction Problems on Triangular Grids.
Applied Science and Engineering Progress, 12(4):1–8, 2019.

[10] R. Eymard, P. Feron, and C. Guichard.
Family of convergent numerical schemes for the incompressible Navier-Stokes equations.
Mathematics and Computers in Simulation, 144:196–218, Feb. 2018.

[11] R. Eymard and C. Guichard.
Discontinuous Galerkin gradient discretisations for the approximation of second-order differential operators in divergence form.
C. Comp. Appl. Math., 37(4):4023–4054, 2018.