Stability of the Lagrange-Galerkin method with non-exact integration

K. W. Morton; A. Priestley; E. Suli

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique (1988)

  • Volume: 22, Issue: 4, page 625-653
  • ISSN: 0764-583X

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Morton, K. W., Priestley, A., and Suli, E.. "Stability of the Lagrange-Galerkin method with non-exact integration." ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique 22.4 (1988): 625-653. <http://eudml.org/doc/193544>.

@article{Morton1988,
author = {Morton, K. W., Priestley, A., Suli, E.},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique},
keywords = {area-weighting quadrature; numerical examples; Lagrange-Galerkin finite element method; linear advection problem; unconditional stability; convergence},
language = {eng},
number = {4},
pages = {625-653},
publisher = {Dunod},
title = {Stability of the Lagrange-Galerkin method with non-exact integration},
url = {http://eudml.org/doc/193544},
volume = {22},
year = {1988},
}

TY - JOUR
AU - Morton, K. W.
AU - Priestley, A.
AU - Suli, E.
TI - Stability of the Lagrange-Galerkin method with non-exact integration
JO - ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique
PY - 1988
PB - Dunod
VL - 22
IS - 4
SP - 625
EP - 653
LA - eng
KW - area-weighting quadrature; numerical examples; Lagrange-Galerkin finite element method; linear advection problem; unconditional stability; convergence
UR - http://eudml.org/doc/193544
ER -

References

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  2. [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. Zbl0508.76049MR706421
  3. [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. Zbl0508.76007MR706421
  4. [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. Zbl0728.65086
  5. [5] A. J. CHORIN & K. W. MORTON, A Mathematical Introduction to Fluid Mechanics (Universitext). Springer-Verlag, New York, Berlin, Heidelberg, Tokyo, 1984. Zbl0417.76002
  6. [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. Zbl0492.65051MR672564
  7. [7] J. W. EASTWOOD, Privarte communication. 
  8. [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. [9] R. W. HOCKNEY & J. W. EASTWOOD, Computer Simulation Using Particles. McGraw-Hill, New York, 1981. Zbl0662.76002
  10. [10] Z. KOPAL, Numerical Analysis. Chapman & Hall Ltd. London, 1961. Zbl0101.33701
  11. [11] I. V. KRYLOV, Approximate Calculation of Integrals. Mac Millan, New York, 1962. Zbl0111.31801MR144464
  12. [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. Zbl0435.76010MR658144
  13. [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. [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. Zbl0632.76077
  15. [15] O. PIRONNEAU, On the transport diffusion algorithm and its application to the Navier-Stokes equations, Numer. Math., 38 (1982), pp. 309-332. Zbl0505.76100MR654100
  16. [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. Zbl0594.76087
  17. [17] E. SÜLI, Convergence and nonlinear stability of the Lagrange-Galerkin method for the Navier-Stokes equations, Numer. Math., 53 (1988), pp. 459-483. Zbl0637.76024MR951325

Citations in EuDML Documents

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  1. Konstantinos Chrysafinos, Noel J. Walkington, Lagrangian and moving mesh methods for the convection diffusion equation
  2. Jozef Kacur, Roger Van Keer, Solution of contaminant transport with adsorption in porous media by the method of characteristics
  3. Jozef Kacur, Roger Van Keer, Solution of contaminant transport with adsorption in porous media by the method of characteristics
  4. Sébastien Boyaval, Tony Lelièvre, Claude Mangoubi, Free-energy-dissipative schemes for the Oldroyd-B model

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