The Runge-Kutta local projection P 1 -discontinuous-Galerkin finite element method for scalar conservation laws

Bernardo Cockburn; Chi-Wang Shu

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

  • Volume: 25, Issue: 3, page 337-361
  • ISSN: 0764-583X

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Cockburn, Bernardo, and Shu, Chi-Wang. "The Runge-Kutta local projection $P^1$-discontinuous-Galerkin finite element method for scalar conservation laws." ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique 25.3 (1991): 337-361. <http://eudml.org/doc/193630>.

@article{Cockburn1991,
author = {Cockburn, Bernardo, Shu, Chi-Wang},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique},
keywords = {hyperbolic conservation laws; discontinuous Galerkin finite element; total variation diminishing Runge-Kutta time discretization; local projection; global stability; maximum principle; entropy solution; order of convergence},
language = {eng},
number = {3},
pages = {337-361},
publisher = {Dunod},
title = {The Runge-Kutta local projection $P^1$-discontinuous-Galerkin finite element method for scalar conservation laws},
url = {http://eudml.org/doc/193630},
volume = {25},
year = {1991},
}

TY - JOUR
AU - Cockburn, Bernardo
AU - Shu, Chi-Wang
TI - The Runge-Kutta local projection $P^1$-discontinuous-Galerkin finite element method for scalar conservation laws
JO - ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique
PY - 1991
PB - Dunod
VL - 25
IS - 3
SP - 337
EP - 361
LA - eng
KW - hyperbolic conservation laws; discontinuous Galerkin finite element; total variation diminishing Runge-Kutta time discretization; local projection; global stability; maximum principle; entropy solution; order of convergence
UR - http://eudml.org/doc/193630
ER -

References

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  2. [2] G. CHAVENT and B. COCKBURN, Consistance et Stabilité des Schémas LRG pour les Lois de Conservation Scalaires, INRIA report # 370 (1987). 
  3. [3] G. CHAVENT and B. COCKBURN, The Local Projection Discontinuons Galerkin Finite Element Method for Scalar Conservation Laws, M2AN, 23 (1989), pp. 565-592. Zbl0715.65079MR1025072
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  8. [8] P. D. LAX and B. WENDROFF, Systems of Conservation Laws, Comm. Pure and Appl. Math., 13 (1960), pp. 217-237. Zbl0152.44802MR120774
  9. [9] S. OSHER, Riemman Solvers, the Entropy Condition, and Difference Approximations, SIAM J. Numer. Anal., 21 (1984), pp. 217-235. Zbl0592.65069MR736327
  10. [10] B. VAN LEER, Towards the Ultimate Conservative Scheme, VI. A NewApproach to Numerical Convection J. Comput.Phys., 23 (1977), pp. 276-299. Zbl0339.76056
  11. [11] C. W. SHU, TVB uniformly high-order schemes for conservation laws, Math.Comp., 49 (1987), pp. 105-121. Zbl0628.65075MR890256
  12. [12] C. W. SHU and S. OSHER, Efficient Implementation of Essentially Non-Oscillatory Shock-Capturing Schemes, J. Comput. Phys., 77 (1988), pp. 439-471. Zbl0653.65072MR954915

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