no. 1
L 2 -stability of the upwind first order finite volume scheme for the Maxwell equations in two and three dimensions on arbitrary unstructured meshes
ESAIM: Modélisation mathématique et analyse numérique, Tome 34 (2000) no. 1, pp. 139-158. 
@article{M2AN_2000__34_1_139_0,
     author = {Piperno, Serge},
     title = {$L^2$-stability of the upwind first order finite volume scheme for the {Maxwell} equations in two and three dimensions on arbitrary unstructured meshes},
     journal = {ESAIM: Mod\'elisation math\'ematique et analyse num\'erique},
     pages = {139--158},
     publisher = {Dunod},
     address = {Paris},
     volume = {34},
     number = {1},
     year = {2000},
     mrnumber = {1735972},
     zbl = {0949.65104},
     language = {en},
     url = {http://www.numdam.org/item/M2AN_2000__34_1_139_0/}
}
TY  - JOUR
AU  - Piperno, Serge
TI  - $L^2$-stability of the upwind first order finite volume scheme for the Maxwell equations in two and three dimensions on arbitrary unstructured meshes
JO  - ESAIM: Modélisation mathématique et analyse numérique
PY  - 2000
SP  - 139
EP  - 158
VL  - 34
IS  - 1
PB  - Dunod
PP  - Paris
UR  - http://www.numdam.org/item/M2AN_2000__34_1_139_0/
LA  - en
ID  - M2AN_2000__34_1_139_0
ER  - 
%0 Journal Article
%A Piperno, Serge
%T $L^2$-stability of the upwind first order finite volume scheme for the Maxwell equations in two and three dimensions on arbitrary unstructured meshes
%J ESAIM: Modélisation mathématique et analyse numérique
%D 2000
%P 139-158
%V 34
%N 1
%I Dunod
%C Paris
%U http://www.numdam.org/item/M2AN_2000__34_1_139_0/
%G en
%F M2AN_2000__34_1_139_0
Piperno, Serge. $L^2$-stability of the upwind first order finite volume scheme for the Maxwell equations in two and three dimensions on arbitrary unstructured meshes. ESAIM: Modélisation mathématique et analyse numérique, Tome 34 (2000) no. 1, pp. 139-158. http://www.numdam.org/item/M2AN_2000__34_1_139_0/

[1] J.J. Ambrosiano, S.T. Brandon, R. Löhner and C.R. Devore, Electromagnetics via the Taylor-Galerkin finite element method on unstructured grids. J. Comput. Phys. 110 (1994) 310-319. | Zbl

[2] D.A. Anderson, J.C. Tannehill and R.H. Pletcher, Computational fluid mechanics and heat transfer, Hemisphere, McGraw-Hill, New York (1984). | MR | Zbl

[3] F. Bourdel, P.-A. Mazet and P. Helluy, Resolution of the non-stationary or harmonic Maxwell equations by a discontinuous finite element method. Application to an E.M.I. (electromagnetic impulse) case. Computing Methods in Applied Sciences and Engineering. Nova Science Publishers, Inc., New-York (1991) 405-422.

[4] P.G. Ciarlet and J.-L. Lions Eds., Handbook of Numerical Analysis, Vol. 1. North Holland-Elsevier Science Publishers, Amsterdam, New York, Oxford (1991). | MR | Zbl

[5] J.-P. Cioni, L. Fezoui and H. Steve, Approximation des équations de Maxwell par des schémas décentrés en éléments finis. Technical Report RR-1601, INRIA (1992).

[6] J.-P. Cioni and M. Remaki, Comparaison de deux méthodes de volumes finis en électromagnétisme. Technical Report RR-3166, INRIA (1997).

[7] J.-P. Cioni, L. Fezoui, L. Anne and F. Poupaud, A parallel FVTD Maxwell solver using 3D unstructured meshes, in 13th annual review of progress in applied computational electromagnetics, Monterey, California (1997).

[8] G. Cohen and P. Joly Eds., Aspects récents en méthodes numériques pour les équations de Maxwell, Collection didactique INRIA, INRIA Rocquencourt, France (1998) 23-27.

[9] S. Depeyre, Étude de schémas d'ordre élevé en volumes finis pour des problèmes hyperboliques. Application aux équations de Maxwell, d'Buler et aux écoulements diphasiques dispersés. Mathématiques appliquées, ENPC, janvier (1997).

[10] R. Eymard, T. Gallouët and R. Herbin, The finite volume method. in Handbook for Numerical Analysis, North Holland-Elsevier Science Publishers, Amsterdam, New York, Oxford (to appear). | MR | Zbl

[11] L. Fezoui and B. Stoufflet, A class of implicit upwind schemes for euler simulations with unstructured meshes. J. Comput. Phys. 84 (1989) 174-206. | MR | Zbl

[12] A. Harten, High Resolution Schemes for Hyperbolic Conservation Laws. J. Comput. Phys. 49 (1983) 357-393. | MR | Zbl

[13] A. Harten, P.D. Lax and B. Van Leer, On upstream differencing and Godunov-type schemes for hyperbolic conservation laws, SIAM Rev. 25 (1983) 36-61. | MR | Zbl

[14] A. Jameson, Artificial diffusion, upwind biasing, limiters and their effect on accuracy and multigrid convergence in transonic and hypersonic flows, in 11th AIAA Computational Fluid Dynamics Conference, Orlando, Florida, July 6-9 (1993), AIAA paper 93-3359.

[15] P. Lesaint, Sur la résolution des systèmes hyperboliques du premier ordre par des méthodes d'éléments finis. Ph.D. thesis, Université de Paris VI, France (1975).

[16] R. Löhner and J. Ambrosiano, A finite element solver for the Maxwell equations, in GAMNI-SMAI Conference on Numerical Methods for the Maxwell Equations, Paris, France (1989). SIAM, Philadelphia (1991).

[17] M. Remaki, A new finite volume scheme for solving Maxwell System. Technical Report RR-3725, INRIA (1999). | Zbl

[18] M. Remaki, L. Fezoui and F. Poupaud, Un nouveau schéma de type volumes finis appliqué aux équations de Maxwell en milieu hétérogène. Technical Report RR-3351, INRIA (1998).

[19] J.S. Shang, A characteristic-based algorithm for solving 3D, time-domain Maxwell equations. In 30th Aerospace Sciences Meeting and Exhibit, Reno, Nevada. January 6-9 (1992), AIAA paper 92-0452.

[20] J.S. Shang and R.M. Fithen, A comparative study of characteristic-based algorithms for the Maxwell equations. J. Comput. Phys. 125 (1996) 378-394. | MR | Zbl

[21] V. Shankar, W.F. Hall and A.H. Mohammadian, A time-domain differential solver for electromagnetic scattering problems. Proc. IEEE 77 (1989) 709-720.

[22] A. Tafiove, Re-inventing electromagnetics: supercomputing solution of Maxwell's equations via direct time integration on space grids. AIAA paper 92-0333 (1992).

[23] K.R. Umashankar, Numerical analysis of electromagnetic wave scattering and interaction based on frequency-domain integral equation and method of moments techniques. Wave Motion 10 (1988) 493. | MR | Zbl

[24] B. Van Leer, Towards the ultimate conservative difference scheme v: a second-order sequel to Godunov's method. J. Comput. Phys. 32 (1979) 361-370. | MR | Zbl

[25] J.-P. Vila, Convergence and error estimates in finite volume schemes for general multidimensional scalr conservation laws. I. Explicite monotone schemes. RAIRO Modél. Math. Anal. Numér. 28 (1994) 267-295. | Numdam | MR | Zbl

[26] J.-P. Vila and P. Villedieu, Convergence de la méthode des volumes finis pour les systèmes de Friedrichs. C.R. Acad. Sci. Paris Sér. I Math. 3(325) (1997) 671-676. | MR | Zbl

[27] R.F. Warming and F. Hyett, The modified equation approach to the stability and accuracy analysis of finite-difference methods. J. Comput. Phys. 14 (1974) 159-179. | MR | Zbl

[28] K.S. Yee, Numerical solution of initial boundary value problems involving Maxwell's equations in isotropic media. IEEE Trans. Antennas and Propagation AP-16 (1966) 302-307. | Zbl