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Une note sur les méthodes de caractéristiques et de Lesaint-Raviart pour les problèmes hyperboliques stationnaires. (A note on the methods of characteristics and of Lesaint-Raviart for stationary hyperbolic problems). (French) Zbl 0687.65088
Cette montre que la méthode de P. Lesaint et P. A. Raviart [On a finite element method for solving the neutron transport equations. Mathematical aspects of finite elements in partial differential equations, 89-123 (1974; MR 58,31918)] dans le cas des problèmes hyperboliques stationnaires, est un cas limite de la méthode des caractéristiques introduite par A. Bermudez et J. Durany [RAIRO, Modalisation Math. Anal. Numer. 21, 7-26 (1987; Zbl 0613.65121)].
Reviewer: M.Sibony

MSC:
65M25 Numerical aspects of the method of characteristics for initial value and initial-boundary value problems involving PDEs
35L70 Second-order nonlinear hyperbolic equations
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References:
[1] J. P. BENQUE, J. RONAT, Quelques difficultés des modèles numériques en hydraulique, Fifth Int. Symposium on Computing Methods in Applied Sciences and Engineering, Versailles, Rapport E.D.F. E/41/82/03. Zbl0505.76035 · Zbl 0505.76035
[2] P. LESAINT, P. A. RAVIART, < On a Finite Element Method for Solving theNeutron Transport Equations > , dans Mathematical Aspects of Finite Eléments in Partial Differential Equations (C. de Boor Ed.), pp. 89-123, Academic Press (1974). Zbl0341.65076 MR658142 · Zbl 0341.65076
[3] C. JOHNSON, U. NAVERT, J. PITKARANTA, Finite Element Methods for Linear Hyperbolic Problems, Comp. Meth. Appl. Mech. Eng, 45, pp. 285-312 (1984). Zbl0526.76087 MR759811 · Zbl 0526.76087 · doi:10.1016/0045-7825(84)90158-0
[4] [4] A. BERMUDEZ, J. DURANY, La méthode des caractéristiques pour les problèmes de convection-diffusion stationnaires, M2AN, vol. 21, n^\circ 1, pp. 7-26 (1987). Zbl0613.65121 MR882685 · Zbl 0613.65121 · eudml:193498
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