Stability of the Lagrange-Galerkin method with non-exact integration
Morton, K. W. ; Priestley, A. ; Suli, E.
ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique, Tome 22 (1988), p. 625-653 / Harvested from Numdam
@article{M2AN_1988__22_4_625_0,
     author = {Morton, K. W. and Priestley, A. and Suli, E.},
     title = {Stability of the Lagrange-Galerkin method with non-exact integration},
     journal = {ESAIM: Mathematical Modelling and Numerical Analysis - Mod\'elisation Math\'ematique et Analyse Num\'erique},
     volume = {22},
     year = {1988},
     pages = {625-653},
     mrnumber = {974291},
     zbl = {0661.65114},
     language = {en},
     url = {http://dml.mathdoc.fr/item/M2AN_1988__22_4_625_0}
}
Morton, K. W.; Priestley, A.; Suli, E. Stability of the Lagrange-Galerkin method with non-exact integration. ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique, Tome 22 (1988) pp. 625-653. http://gdmltest.u-ga.fr/item/M2AN_1988__22_4_625_0/

[1] M. Abramowitz & A. Stegun, Handbook of Mathematical Functions. Dover Publications Inc., New York, 1965.

[2] J. P. Benque, G. Labadie & J. Ronat, A new finite element method for the Navier-Stokes equations coupled with a temperature equation. Proc. 4th Int. Symp. on Finite Element Methods in Flow Probiems (Ed. T. Kawai), North-Holland, Amsterdam, Oxford, New York, 1982, pp. 295-301. | MR 706421 | Zbl 0508.76049

[3] M. Bercovier & O. Pironneau, Characteristics and the finite element method. Proc. 4th Int. Symp. on Finite Element Methods in Flow Problems (Ed. T. Kawai), North-Holland, Amsterdam, Oxford, New York, 1982, pp. 67-63. | MR 706421 | Zbl 0508.76007

[4] P. N. Childs & K. W. Morton, Characteristic Galerkin methods for scalar conservation laws in on dimension. Oxford University Computing Laboratory Report No. 86/5, 1986. To appear in SIAM J. Numerical Analysis. | Zbl 0728.65086

[5] A. J. Chorin & K. W. Morton, A Mathematical Introduction to Fluid Mechanics (Universitext). Springer-Verlag, New York, Berlin, Heidelberg, Tokyo, 1984. | Zbl 0417.76002

[6] J. Douglas Jr & T. F. Russell, Numerical methods for convention-dominated diffusion problems based on combining the method of characteristics with finite element or finite difference procedures. SIAM J. Numer. Anal., 19 (1982), pp. 871-885. | MR 672564 | Zbl 0492.65051

[7] J. W. Eastwood, Privarte communication.

[8] F. H. Harlow, The particle in celle computing method for fluid dynamics. Methods in Computational Physis (Ed. B. Adler, S. Fernbach & M. Rotenberg), Vol. 3, Academic Press, New York, 1964.

[9] R. W. Hockney & J. W. Eastwood, Computer Simulation Using Particles. McGraw-Hill, New York, 1981. | Zbl 0662.76002

[10] Z. Kopal, Numerical Analysis. Chapman & Hall Ltd. London, 1961. | Zbl 0101.33701

[11] I. V. Krylov, Approximate Calculation of Integrals. Mac Millan, New York, 1962. | MR 144464 | Zbl 0111.31801

[12] P. Lesaint, Numerical solution of the equation of continuity. Topics in Numerical Analysis III (Ed. J. J. H. Miller), Academic Press, London, New York, San Francisco, 1977, pp. 199-222. | MR 658144 | Zbl 0435.76010

[13] K. W. Morton & A. Priestley, On characteristic and Lagrange-Galerkin methods. Pitman Research Notes in Mathematics Series (Ed. D. F. Griffiths & G. A. Watson), Longman Scientific and Technical, Harlow, 1986.

[14] K. W. Morton & P. Sweby, A comparison of flux limited difference methods and characteristic Galerkin methods for shock modelling. To appear in J. Comput. Phys. | Zbl 0632.76077

[15] O. Pironneau, On the transport diffusion algorithm and its application to the Navier-Stokes equations, Numer. Math., 38 (1982), pp. 309-332. | MR 654100 | Zbl 0505.76100

[16] T. F. Russell, Time stepping along characteristics with incomplete iteration for a Galerin approcimation of miscible displacement in porus media. Ph. D. Thesis, University of Chicago, 1980. | Zbl 0594.76087

[17] E. Süli, Convergence and nonlinear stability of the Lagrange-Galerkin method for the Navier-Stokes equations, Numer. Math., 53 (1988), pp. 459-483. | MR 951325 | Zbl 0637.76024