Reduced continuity finite element methods for first order scalar hyperbolic equations
ESAIM: Modélisation mathématique et analyse numérique, Tome 28 (1994) no. 6, pp. 667-698. 
@article{M2AN_1994__28_6_667_0,
     author = {Cai, D.-M. and Falk, R. S.},
     title = {Reduced continuity finite element methods for first order scalar hyperbolic equations},
     journal = {ESAIM: Mod\'elisation math\'ematique et analyse num\'erique},
     pages = {667--698},
     publisher = {AFCET - Gauthier-Villars},
     address = {Paris},
     volume = {28},
     number = {6},
     year = {1994},
     mrnumber = {1302419},
     zbl = {0821.65068},
     language = {en},
     url = {http://archive.numdam.org/item/M2AN_1994__28_6_667_0/}
}
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Cai, D.-M.; Falk, R. S. Reduced continuity finite element methods for first order scalar hyperbolic equations. ESAIM: Modélisation mathématique et analyse numérique, Tome 28 (1994) no. 6, pp. 667-698. http://archive.numdam.org/item/M2AN_1994__28_6_667_0/

[1] D. Cai, Reduced continuity finite element methods for hyperbolic equations, Ph. D. Dissertation, Rutgers University, 1991.

[2] P. G. Ciarlet, The Fintie Element Method for Elliptic Equations, North-Holland, Amsterdam, 1978. | MR

[3] R. S. Falk and G. R. Richter, Analysis of a continuous fimte element method for hyperbolic equations, SIAM J. Numer. Anal., 24 (1987), pp. 257-278. | MR | Zbl

[4] R. S. Falk and G. R. Richter, Local estimates for a finite element method for hyperbolic and convection-diffusion equations, SIAM J. Numer. Anal., 29 (1992), pp. 730-754. | MR | Zbl

[5] M. Fortin and M. Soulie, A non-conforming piecewise quadratic finite element on triangles, Internat. J. Numer. Methods Engrg, 19 (1983), pp. 505-520. | MR | Zbl

[6] T. J. R. Hughes and A. Brooks, A multidimensional upwind scheme with no crosswind diffusion, in Finite Element Methods for Convection Dominated Flows (T. J. R. Hughes, ed.), AMD (ASME), 1979, pp. 19-35. | MR | Zbl

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

[8] C. Johnson and J. Pitkäranta, An analysis of the discontinuous Galerkin method for a scalar hyperbolic equation, Math. Comp., 46 (1986), pp. 1-26. | MR | Zbl

[9] P. Lesaint and P. A. Raviart, On a finite element method for solving the neutron transport equations, in Mathematical Aspects of Finite Elements in Partial Differential Equations (C. de Boor), ed.), Academis Press, New York, 1974, pp. 89-123. | MR | Zbl

[10] W. H. Reed and T. R. Hill, Triangular mesh methods for the neutron transport equation, Los Alamos Scientific Laboratory, Report LA-UR-73-479 (1973).

[11] G. R. Richter, An optimal-order error estimate for the discontinuous Galerkin method, Math. Comp., 50 (1988), pp. 75-88. | MR | Zbl

[12] R. Winther, A stable finite element method for first-order hyperbolic systems, Math. Comp., 36 (1981), pp. 65-86. | MR | Zbl