An explicit stable numerical scheme  for the $1D$ transport equation

Yohan Penel

doi:10.3934/dcdss.2012.5.641

journal article Jan 01, 2012

An explicit stable numerical scheme for the $1D$ transport equation

Discrete and Continuous Dynamical Systems - S Vol. 5 No. 3 pp. 641-656 · American Institute of Mathematical Sciences (AIMS)

View at Publisher Save 10.3934/dcdss.2012.5.641

Topics

No keywords indexed for this article. Browse by subject →

References

16

[1]

C. Bardos, M. Bercovier and O. Pironneau, The vortex method with finite elements, Math. Comp., 36 (1981), 119-136. 10.1090/s0025-5718-1981-0595046-3

[2]

F. Boyer and P. Fabrie, "Éléments d'Analyse pour l'Étude de Quelques Modèles d'Écoulements de Fluides Visqueux Incompressibles,'' Mathématiques & Applications (Berlin), 52, Springer-Verlag, Berlin, 2006. 10.1007/3-540-29819-3

[3]

J. Burgers, "A Mathematical Model Illustrating the Theory of Turbulence," edited by Richard von Mises and Theodore von Kármán, Adv. Appl. Mech., Academic Press, Inc., New York, (1948), 171-199. 10.1016/s0065-2156(08)70100-5

[4]

S. Dellacherie, On a diphasic low Mach number system, M2AN Math. Model. Numer. Anal., 39 (2005), 487-514. 10.1051/m2an:2005020

[5]

B. Després and F. Lagoutière, Contact discontinuity capturing schemes for linear advection and compressible gas dynamics, J. Sci. Comput., 16 (2001), 479-524. 10.1023/a:1013298408777

[6]

J. Douglas Jr. and T. Russell, Numerical methods for convection-dominated diffusion problems based on combining the method of characteristics with finite element or finite difference procedures, SIAM J. Numer. Anal., 19 (1982), 871-885. 10.1137/0719063

[7]

J. Douglas Jr., C.-S. Huang and F. Pereira, The modified method of characteristics with adjusted advection, Numer. Math., 83 (1999), 353-369. 10.1007/s002110050453

[8]

G. Fourestey, "Simulation Numérique et Contrôle Optimal d'Interactions Fluide Incompressible/Structure par une Méthode de Lagrange-Galerkin d'Ordre 2,'' Ph.D Thesis, École Nationale des Ponts et Chaussées, 2002. Available at: <a href="http://hal.archives-ouvertes.fr/tel-00005675" target="_blank">http://hal.archives-ouvertes.fr/tel-00005675</a>.

[9]

E. Godlewski and P.-A. Raviart, "Numerical Approximation of Hyperbolic Systems of Conservation Laws,'' Applied Mathematical Sciences, 118, Springer-Verlag, New York, 1996. 10.1007/978-1-4612-0713-9

[10]

F. Holly and A. Preissmann, Accurate calculation of transport in two dimensions, J. Hydr. Div., 103 (1977), 1259-1277. 10.1061/jyceaj.0004870

[11]

R. LeVeque, "Numerical Methods for Conservation Laws," Second edition, Lectures in Mathematics ETH Zürich, Birkhäuser Verlag, Basel, 1992. 10.1007/978-3-0348-8629-1

[12]

J. Marsden and A. Chorin, "A Mathematical Introduction to Fluid Mechanics," Springer-Verlag, New-York-Heidelberg, 1979.

[13]

Fronts propagating with curvature-dependent speed: Algorithms based on Hamilton-Jacobi formulations

Stanley Osher, James A Sethian

Journal of Computational Physics 10.1016/0021-9991(88)90002-2

[14]

Ph.D Thesis, Univ. Paris 13, Available at: <a href="http://hal.archives-ouvertes.fr/tel-00547865" target="_blank">http://hal.archives-ouvertes.fr/tel-00547865</a>.

[15]

Submitted.

[16]

Numer. Math., 38 (1981/82), 309-332. 10.1007/bf01396435

Metrics

3

Citations

16

References

Details

Published: Jan 01, 2012
Vol/Issue: 5(3)
Pages: 641-656

Authors

Y

Yohan Penel

Cite This Article

Yohan Penel (2012). An explicit stable numerical scheme for the $1D$ transport equation. Discrete and Continuous Dynamical Systems - S, 5(3), 641-656. https://doi.org/10.3934/dcdss.2012.5.641

An explicit stable numerical scheme for the $1D$ transport equation

You May Also Like