Convergence of a streamline diffusion finite element method for scalar conservation laws with boundary conditions
Szepessy, A.
ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique, Tome 25 (1991), p. 749-782 / Harvested from Numdam
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@article{M2AN_1991__25_6_749_0,
     author = {Szepessy, A.},
     title = {Convergence of a streamline diffusion finite element method for scalar conservation laws with boundary conditions},
     journal = {ESAIM: Mathematical Modelling and Numerical Analysis - Mod\'elisation Math\'ematique et Analyse Num\'erique},
     volume = {25},
     year = {1991},
     pages = {749-782},
     mrnumber = {1135992},
     zbl = {0751.65061},
     language = {en},
     url = {http://dml.mathdoc.fr/item/M2AN_1991__25_6_749_0}
}

Szepessy, A. Convergence of a streamline diffusion finite element method for scalar conservation laws with boundary conditions. ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique, Tome 25 (1991) pp. 749-782. http://gdmltest.u-ga.fr/item/M2AN_1991__25_6_749_0/

[BLN] C. Bardos, A. Y. Le Roux, J. C. Nedelec, First order quasilinear equations with boundary conditions, Comm. P.D.E. 4 (9), pp. 1017-1034, 1979. | MR 542510 | Zbl 0418.35024

[Di] R. J. Diperna, Measure-valued solutions of conservation laws, Arch. Rat. Mech. Anal. 8 (1985). | MR 775191 | Zbl 0616.35055

[Di2] R. J. Diperna, Convergence of approximate solutions to conservation laws, Arch. Rat. Mech. Anal. 82 (1983), 27-70. | MR 684413 | Zbl 0519.35054

[DL] F. Dubois et P. Le Floch, C. R. Acad., Sci. Paris 304, sériel (1987) 75-78. | MR 878830 | Zbl 0634.35046

[H] T. J. R. Hughes and M. Mallet, A new finite element formulation for computational fluid dynamics : IV. a discontinuity - capturing operator for multidimensional advective - diffusive Systems, Comput. Methods Appl. Mech. Engrg. 58 (1986) 329-336. | MR 865672 | Zbl 0587.76120

[JNP] C. Johnson, U. Nävert and J. Pitkäranta, Finite element methods for linear hyperbolic problems, Comput. Methods Appl. Mech. Engrg. 45 (1984) 285-312. | MR 759811 | Zbl 0526.76087

[JS] C. Johnson and J. Saranen, Streamline diffusion methods for problems in fluid mechanics, Math. Comp. v. 47 (1986) pp.1-18. | MR 842120 | Zbl 0609.76020

[JSz I] C. Johnson and A. Szepessy, On the convergence of a finite element method for a nonlinear hyperbolic conservation law, Math. Comp., vol.49, n° 180, oct. 1987, pp. 427-444. | MR 906180 | Zbl 0634.65075

[JSz II] C. Johnson, A. Szepessy and P. Hansbo On the convergence of shock-capturing streamline diffusion finite element methods for hyperbolic conservation laws, Math. Comp. 54 (1990) 82-107. | MR 995210 | Zbl 0685.65086

[Lax] P. D. Lax, Shock waves and entropy, in Contributions to Nonlinear Functional Analysis, ed. E. A. Zarantonello, Academic Press (1971), 603-634. | MR 393870 | Zbl 0268.35014

[LR I] A. Y. Le Roux, Étude du problème mixte pour une équation quasi linéaire du premier ordre, C. R. Acad. Sci. Paris, t. 285, Série A-351. | MR 442449 | Zbl 0366.35019

[LR II] A. Y. Le Roux, Approximation de quelques problèmes hyperboliques non linéaires, Thèse d'État, Rennes, 1979.

[Li] J. L. Lions, Quelques Méthodes de Résolution des Problèmes aux Limites non Linéaires, Paris, 1969. | MR 259693 | Zbl 0189.40603

[Sz I] A. Szepessy, Convergence of a shock-capturing streamline diffusion finite element method for scalar conservation laws in two space dimensions, Math. Comp., Oct. 1989, 527-545. | MR 979941 | Zbl 0679.65072

[Sz II] A. Szepessy, An existence result for scalar conservation laws using measure valued solutions, Comm. PDE, 14 (10), 1989, 1329-1350. | MR 1022989 | Zbl 0704.35022

[Sz III] A. Szepessy, Measure valued solutions of scalar conservation laws with boundary conditions, Arch. Rational Mech. Anal. 107, n°2, 1989, 181-193. | MR 996910 | Zbl 0702.35155

[Sz IV] A. Szepessy, Convergence of the Streamline Diffusion Finite Element Method for Conservation Laws, Thesis (1989), Dept. of Math., Chalmers Univ., S-41296 Göteborg.

[Ta] L. Tartar, The Compensated Compactness Method Applied to Systems of Conservation Laws, J. M. Bail (ed.), Systems of Nonlinear Partial Differential Equations, 263-285. NATO ASI series C, Reidel Publishing Col. (1983). | MR 725524 | Zbl 0536.35003