Finite element approximation of the transport of reactive solutes in porous media. part II: Error estimates for equilibrium adsorption processes

SIAM Journal on Numerical Analysis

Volumn 34, Issue 2, 1997, Pages 455-479

  Barrett, John W ^a   Knabner, Peter ^b,c  

^a IMPERIAL COLLEGE LONDON   (United Kingdom)

^b Inst F Angew Anal Und Stochastik   (Germany)

^c UNIVERSITY OF ERLANGEN NUREMBERG   (Germany)

Author keywords

Degenerate parabolic problem; Error analysis; Finite elements; Porous medium

Indexed keywords

EID: 0001035419     PISSN: 00361429     EISSN: None     Source Type: Journal    
DOI: 10.1137/S0036142993258191     Document Type: Article

References (16)

1. D. G. ARONSON, The porous medium equation, in Nonlinear Diffusion Problems, Lecture Notes in Mathematics 1224, Springer-Verlag, Berlin, 1986, pp. 1-46.
2. D. G. ARONSON, L. A. CAFFARELLI, AND S. KAMIN, How an initially stationary interface begins to move in porous medium flow, SIAM J. Math. Anal., 14 (1983), pp. 639-658.
3. J. W. BARRETT AND P. KNABNER, Finite element approximation of transport of reactive solutes in porous media. Part I: Error estimates for non-equilibrium adsorption processes, SIAM J. Numer. Anal., 34 (1997), pp. 201-227.
4. J. W. BARRETT AND P. KNABNER, Finite element approximation of transport of reactive solutes in porous media: Part 2 Error estimates for equilibrium adsorption processes, Preprint no. 69, Institute für Angewandte Analysis und Stochastik, Berlin, Germany, 1993.
5. J. W. BARRETT AND R. M. SHANAHAN, Finite element approximation of a model reaction-diffusion problem with a non-Lipschitz nonlinearity, Numer. Math., 59 (1991), pp. 217-242.
6. C. M. ELLIOTT, Error analysis of the enthalpy method for the Stefan problem, IMA J. Numer. Anal., 7 (1987), pp. 61-71.
7. W. JÄGER AND J. KAČUR, Solution of porous medium type systems by linear approximation schemes, Numer. Math., 60 (1991), pp. 407-427.
8. A. KUFNER, O. JOHN, AND S. FUČIK, Function Spaces, P. Nordhoff, Groningen, The Netherlands, 1977.
9. R. H. NOCHETTO, Sharp L-error estimates for semilinear elliptic problems with free boundaries, Numer. Math., 54 (1988), pp. 243-255.
10. R. H. NOCHETTO, Finite element methods for parabolic free boundary problems, in Advances in Numerical Analysis, Vol. 1, W. Light, ed., Oxford University Press, London, UK, 1991, pp. 34-95.
11. R. H. NOCHETTO AND C. VERDI, Approximation of degenerate parabolic problems using numerical integration, SIAM J. Numer. Anal., 25 (1988), pp. 784-814.
12. L. A. PELETIER, A necessary and sufficient condition for the existence of an interface in flows through porous media, Arch. Rational Mech. Anal., 56 (1974), pp. 183-190.
13. P. E. SACKS, The initial and boundary value problem for a class of degenerate parabolic equations, Comm. Partial Differential Equations, 8 (1983), pp. 693-733.
14. V. THOMÉE, Galerkin Finite Element Methods for Parabolic Problems, Springer-Verlag, Berlin, 1984.
15. C. VERDI AND A. VISINTIN, Error estimates for a semi-explicit numerical scheme for Stefantype problems, Numer, Math., 52 (1988), pp. 165-185.
16. M. WATANABE, Solutions with compact support of the porous medium equation in arbitrary dimensions, Proc. Amer. Math. Soc., 103 (1988), pp. 149-152.