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.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Amiez, G., Gremaud, P.A., On a numerical approach to Stefan-like problems, Nu-mer. Math. 59, 71–89 (1991).
Atthey, D.R. A Finite Difference Scheme for Melting Problems, J. Inst. Math. Appl. 13, 353–366 (1974).
Baughman, L.A., Walkington, N.J., Co-volume methods for degenerate parabolic problems, Numer.Math. 64, 45–67 (1993).
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).
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).
Eymard, R., Gallouët, T., Hilhorst, D., Y. Naït Slimane, Finite volumes and nonlinear diffusion equations, preprint.
Herbin R.: An error estimate for a finite volume scheme for a diffusion convection problem on a triangular mesh, preprint (1994).
Kamenomostskaja, S.L., On the Stefan problem, Mat. Sb. 53 (95), 489–514 ( 1961 in Russian).
Meyer, G.H., Multidimensional Stefan Problems, SIAM J. Num. Anal., 10, 522–538 (1973).
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).
Oleinik, O.A., A method of solution of the general Stefan Problem, Soy. Math. Dokl. 1, 1350–1354, (1960).
Verdi, C., Numerical aspects of parabolic free boundary and hysteresis problems, Phase Transitions and Hysteresis, A. Visinitin ed., Springer-Verlag, 213–284 (1994).
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1998 Springer Science+Business Media Dordrecht
About this chapter
Cite this chapter
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
Download citation
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