Numerical methods with interface estimates for the porous medium equation

 Access to full text

 Full (PDF)

1. [1] C BAIOCCHI, Estimations d’erreur dans $L^{\infty }$ 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