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Convergence of a Finite Volume Scheme for a Parabolic Degenerate Equation

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Recent Advances in Problems of Flow and Transport in Porous Media

Part of the book series: Theory and Applications of Transport in Porous Media ((TATP,volume 11))

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Abstract

In this note we prove the convergence of explicit and implicit finite volume schemes for the numerical solution of the Stefan-type problem u t — Δφ(u) = v, together with the homogeneous Neumann boundary condition.

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References

  1. Amiez, G., Gremaud, P.A., On a numerical approach to Stefan-like problems, Nu-mer. Math. 59, 71–89 (1991).

    Google Scholar 

  2. Atthey, D.R. A Finite Difference Scheme for Melting Problems, J. Inst. Math. Appl. 13, 353–366 (1974).

    Article  Google Scholar 

  3. Baughman, L.A., Walkington, N.J., Co-volume methods for degenerate parabolic problems, Numer.Math. 64, 45–67 (1993).

    Article  Google Scholar 

  4. Berger, A.E., Brezis, H., Rogers, J.C.W., A Numerical Method for Solving the Problem ut — 0 f (u) = 0, RAIRO Numerical Analysis, Vol. 13, 4, 297–312 (1979).

    Google Scholar 

  5. Ciavaldini, J.F., Analyse numérique d’un problème de Stefan à deux phases par une méthode d’éléments finis, SIAM J. Numer. Anal., 12, 464–488 (1975).

    Article  Google Scholar 

  6. Eymard, R., Gallouët, T., Hilhorst, D., Y. Naït Slimane, Finite volumes and nonlinear diffusion equations, preprint.

    Google Scholar 

  7. Herbin R.: An error estimate for a finite volume scheme for a diffusion convection problem on a triangular mesh, preprint (1994).

    Google Scholar 

  8. Kamenomostskaja, S.L., On the Stefan problem, Mat. Sb. 53 (95), 489–514 ( 1961 in Russian).

    Google Scholar 

  9. Meyer, G.H., Multidimensional Stefan Problems, SIAM J. Num. Anal., 10, 522–538 (1973).

    Article  Google Scholar 

  10. Nochetto, R.H., Finite Element Methods for Parabolic Free Boundary Problems, Advances in Numerical Analysis, Vol I: Nonlinear Partial Differential Equations and Dynamical Systems, W. Light ed., Oxford University Press, 34–88 (1991).

    Google Scholar 

  11. Oleinik, O.A., A method of solution of the general Stefan Problem, Soy. Math. Dokl. 1, 1350–1354, (1960).

    Google Scholar 

  12. Verdi, C., Numerical aspects of parabolic free boundary and hysteresis problems, Phase Transitions and Hysteresis, A. Visinitin ed., Springer-Verlag, 213–284 (1994).

    Google Scholar 

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Eymard, R., Gallouët, T., Hilhorst, D., Slimane, Y.N. (1998). Convergence of a Finite Volume Scheme for a Parabolic Degenerate Equation. In: Crolet, J.M., El. Hatri, M. (eds) Recent Advances in Problems of Flow and Transport in Porous Media. Theory and Applications of Transport in Porous Media, vol 11. Springer, Dordrecht. https://doi.org/10.1007/978-94-017-2856-0_1

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  • DOI: https://doi.org/10.1007/978-94-017-2856-0_1

  • Publisher Name: Springer, Dordrecht

  • Print ISBN: 978-90-481-4989-6

  • Online ISBN: 978-94-017-2856-0

  • eBook Packages: Springer Book Archive

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