Numerical methods with interface estimates for the porous medium equation

David Hoff; Bradley J. Lucier

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique (1987)

  • Volume: 21, Issue: 3, page 465-485
  • ISSN: 0764-583X

How to cite

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Hoff, David, and Lucier, Bradley J.. "Numerical methods with interface estimates for the porous medium equation." ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique 21.3 (1987): 465-485. <http://eudml.org/doc/193510>.

@article{Hoff1987,
author = {Hoff, David, Lucier, Bradley J.},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique},
keywords = {numerical approximation; porous-medium equation; error bound; Hölder exponent; weak truncation error; finite-difference scheme},
language = {eng},
number = {3},
pages = {465-485},
publisher = {Dunod},
title = {Numerical methods with interface estimates for the porous medium equation},
url = {http://eudml.org/doc/193510},
volume = {21},
year = {1987},
}

TY - JOUR
AU - Hoff, David
AU - Lucier, Bradley J.
TI - Numerical methods with interface estimates for the porous medium equation
JO - ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique
PY - 1987
PB - Dunod
VL - 21
IS - 3
SP - 465
EP - 485
LA - eng
KW - numerical approximation; porous-medium equation; error bound; Hölder exponent; weak truncation error; finite-difference scheme
UR - http://eudml.org/doc/193510
ER -

References

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  1. [1] C BAIOCCHI, Estimations d’erreur dans L ∞ pour les inéquations à obstacle, in « Mathematical Aspects of Finite Element Methods », Lecture Notes in Mathematics, 606, Springer Verlag, NewYork, in 1977, pp. 27-34. Zbl0374.65053MR488847
  2. [2] L. A. CAFFARELLI and A. FRIEDMAN, Regularity of the free boundary of a gas flow in ann-dimensional porous medium, Indiana Math. J. 29 (1980), 361-391 Zbl0439.76085MR570687
  3. [3] M. G. CRANDALL and L. TARTAR, Some relations between nonexpansive and order preserving mappings, Proc. Amer. Math. Soc.34 (1980), 385-390. Zbl0449.47059MR553381
  4. [4] E. Di BENEDETTO and D. HOFF, An interface tracking algorithm for the porous medium equation, Trans, Amer. Math. Soc.284 (1984), 463-500. Zbl0564.76090MR743729
  5. [5] M. GURTIN, R. MACCAMY and E. SOCOLOVSKY, A coordinate transformation for the porous media equation that renders the free boundary stationary, MRCTech. Rep.2560. Zbl0574.76093
  6. [6] K. HOLLIG and M. PILANT, Regularity of the free boundary for the porous medium equation, MRC Tech. Rep.2742. Zbl0621.35101
  7. [7] J. JEROME, Approximation of Nonlinear Evolution Systems, Academic Press,New York, 1983. Zbl0512.35001MR690582
  8. [8] B. J. LUCIER, On nonlocal monotone difference methods for scalar conservation laws, Math. Comp. 47 (1986), 19-36. Zbl0604.65061MR842121
  9. [9] R. H. NOCHETTO, A note on the approximation of free boundaries by finite element methods, Modélisation Math, et Anal. Num. 20 (1986), 355-368. Zbl0596.65092MR852686
  10. [10] M. E. ROSE, Numerical methods for flows through porous media. I, Math.Comp. 40 (1983), 435-467. Zbl0518.76078MR689465
  11. [11] K. TOMOEDA and M. MIMURA , Numerical approximations to interface curves for a porous media equation, Hiroshima Math. J. 13 (1983), 273-294. Zbl0537.76065MR707183

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