A “natural” norm for the method of characteristics using discontinuous finite elements : 2D and 3D case

Jacques Baranger; Ahmed Machmoum

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique (1999)

  • Volume: 33, Issue: 6, page 1223-1240
  • ISSN: 0764-583X

How to cite

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Baranger, Jacques, and Machmoum, Ahmed. "A “natural” norm for the method of characteristics using discontinuous finite elements : 2D and 3D case." ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique 33.6 (1999): 1223-1240. <http://eudml.org/doc/193969>.

@article{Baranger1999,
author = {Baranger, Jacques, Machmoum, Ahmed},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique},
keywords = {error estimates; first-order stationary hyperbolic equation; method of characteristics; discontinuous finite elements},
language = {eng},
number = {6},
pages = {1223-1240},
publisher = {Dunod},
title = {A “natural” norm for the method of characteristics using discontinuous finite elements : 2D and 3D case},
url = {http://eudml.org/doc/193969},
volume = {33},
year = {1999},
}

TY - JOUR
AU - Baranger, Jacques
AU - Machmoum, Ahmed
TI - A “natural” norm for the method of characteristics using discontinuous finite elements : 2D and 3D case
JO - ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique
PY - 1999
PB - Dunod
VL - 33
IS - 6
SP - 1223
EP - 1240
LA - eng
KW - error estimates; first-order stationary hyperbolic equation; method of characteristics; discontinuous finite elements
UR - http://eudml.org/doc/193969
ER -

References

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  1. [1] J. Baranger and A. Machmoum, Une norme naturelle pour la méthode des caractéristiques en éléments finis discontinus : cas 1-D. RAIRO Modèl. Math, Anal. Numér. 30 (1996) 549-574. Zbl0862.65050MR1411391
  2. [2] J. Baranger and A. Machmoum, Existence of approximate solutions and error bounds for viscoelastic fluid flow: Characteristics method. Comput. Methods Appl. Mech. Engrg. 148 (1997) 39-52. Zbl0923.76098MR1460319
  3. [3] F. Basombrio, Flows in viscoelastic fluids treated by the method of characteristics. J. Non-Newtonian Fluid Mech. 39 (1991)17-34. Zbl0718.76015
  4. [4] A. Bermudez and J. Durany, La méthode des caractéristiques pour les problèmes de convection-diffusion stationnaires. RAIRO Modél. Math. Anal Numér. 21 (1987) 7-26. Zbl0613.65121MR882685
  5. [5] M. Fortin and A. Fortin, Une note sur les méthodes de caractéristiques et de Lesaint-Raviart pour les problèmes hyperboliques stationnaires. RAIRO Modél Math. Anal Numér. 23 (1989) 593-596. Zbl0687.65088MR1025073
  6. [6] M. Fortin and D. Esselaoui, A finite element procedure for viscoelastic flows. Int. J. Numer. Methods Fluids 7 (1987) 1035-1052. Zbl0634.76007
  7. [7] V. Girault and P.A. Raviart, Finite element method for Navier Stokes equations, Theory and Algorithms. Springer, Berlin-Heidelberg-New York (1986). Zbl0585.65077MR851383
  8. [8] C. Johnson and J. Pitkaranta, An analysis of the discontinuous Galerkin method for a scalar hyperbolic equation. Math. Comp. 46 (1987) 1-26. Zbl0618.65105MR815828
  9. [9] P. Lesaint and P.A. Raviart, On a finite element method for solving the neutron transport equations, in Mathematical aspects of finite element in partial differential equations, C. de Boor Ed., Academic Press (1974) 89-123. Zbl0341.65076MR658142
  10. [10] A. Machmoum, Méthodes numériques pour les fluides viscoélastiques : méthode des caractéristiques pour les modèles différentiels et intégraux. Thèse, Université Lyon 1, Laboratoire d'analyse numérique (1996). 
  11. [11] T.E. Paterson, A note on the convergence of the discontinuous Galerkin method for a scalar hyperbolic equation. SIAM J. Numer. Anal. 26 (1991) 133-140. Zbl0729.65085MR1083327

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