Convergence of a streamline diffusion finite element method for scalar conservation laws with boundary conditions

A. Szepessy

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique (1991)

  • Volume: 25, Issue: 6, page 749-782
  • ISSN: 0764-583X

How to cite

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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 25.6 (1991): 749-782. <http://eudml.org/doc/193647>.

@article{Szepessy1991,
author = {Szepessy, A.},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique},
keywords = {convergence; shock-capturing streamline diffusion finite element method; conservation laws; Numerical experiments},
language = {eng},
number = {6},
pages = {749-782},
publisher = {Dunod},
title = {Convergence of a streamline diffusion finite element method for scalar conservation laws with boundary conditions},
url = {http://eudml.org/doc/193647},
volume = {25},
year = {1991},
}

TY - JOUR
AU - Szepessy, A.
TI - Convergence of a streamline diffusion finite element method for scalar conservation laws with boundary conditions
JO - ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique
PY - 1991
PB - Dunod
VL - 25
IS - 6
SP - 749
EP - 782
LA - eng
KW - convergence; shock-capturing streamline diffusion finite element method; conservation laws; Numerical experiments
UR - http://eudml.org/doc/193647
ER -

References

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  8. [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. Zbl0634.65075MR906180
  9. [JSz II] C. JOHNSON, A. SZEPESSY and P. HANSBOOn the convergence of shock-capturing streamline diffusion finite element methods for hyperbolic conservation laws, Math. Comp. 54 (1990) 82-107. Zbl0685.65086MR995210
  10. [Lax] P. D. LAX, Shock waves and entropy, in Contributions to Nonlinear Functional Analysis, ed. E. A. Zarantonello, Academic Press (1971), 603-634. Zbl0268.35014MR393870
  11. [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. Zbl0366.35019MR442449
  12. [LR II] A. Y. LE ROUX, Approximation de quelques problèmes hyperboliques non linéaires, Thèse d'État, Rennes, 1979. 
  13. [Li] J. L. LIONS, Quelques Méthodes de Résolution des Problèmes aux Limites non Linéaires, Paris, 1969. Zbl0189.40603MR259693
  14. [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. Zbl0679.65072MR979941
  15. [Sz II] A. SZEPESSY, An existence result for scalar conservation laws using measure valued solutions, Comm. PDE, 14 (10), 1989, 1329-1350. Zbl0704.35022MR1022989
  16. [Sz III] A. SZEPESSY, Measure valued solutions of scalar conservation laws with boundary conditions, Arch. Rational Mech. Anal. 107, n°2, 1989, 181-193. Zbl0702.35155MR996910
  17. [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. 
  18. [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). Zbl0536.35003MR725524

Citations in EuDML Documents

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  1. J.-P. Vila, Convergence and error estimates in finite volume schemes for general multidimensional scalar conservation laws. I. Explicite monotone schemes
  2. Bruno Després, Frédéric Lagoutière, Generalized Harten formalism and longitudinal variation diminishing schemes for linear advection on arbitrary grids
  3. Bruno Després, Frédéric Lagoutière, Generalized Harten Formalism and Longitudinal Variation Diminishing schemes for Linear Advection on Arbitrary Grids
  4. Sébastien Martin, Julien Vovelle, Convergence of implicit Finite Volume methods for scalar conservation laws with discontinuous flux function
  5. Laurent Levi, Obstacle problems for scalar conservation laws
  6. Yuting Wei, Stabilized finite element methods for miscible displacement in porous media
  7. Laurent Levi, Obstacle problems for scalar conservation laws

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