A numerical approach to degenerate parabolic equations

Numerische Mathematik

Volumn 92, Issue 2, 2002, Pages 357-381

  Pop, Iuliu Sorin ^a   Yong, Wen An ^b  

^a EINDHOVEN UNIVERSITY OF TECHNOLOGY   (Netherlands)

^b UNIVERSITY OF HEIDELBERG   (Germany)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0035982250     PISSN: 0029599X     EISSN: None     Source Type: Journal    
DOI: 10.1007/s002110100330     Document Type: Article

References (24)

1. H.W. Alt, S. Luckhaus: Quasilinear elliptic-parabolic differential equations. Math. Z. 183, 311-341 (1983)
2. T. Arbogast, M. F. Wheeler, N.-Y. Zhang: A nonlinear mixed finite element method for a degenerate parabolic equation arising in flow in porous media. SIAM J. Numer. Anal. 33, 1669-1687 (1996)
3. G. I. Barenblatt: On some unsteady motion of a liquid or a gas in a porous medium. Prikl. Math. Meh. 16, 67-78 (1952)
4. P. Bastian, K. Birken, K. Johannsen, S. Lang, N. Neuss, H. Rentz-Reichert, C. Wieners: UG - a flexible Software toolbox for solving partial differential equations. Computing and Visualization in Science 1, 27-40 (1997)
5. C. Ebmeyer: Error estimates for a class of degenerate parabolic equations. SIAM J. Numer. Anal. 35, 1095-1113 (1998)
6. C. M. Elliott: Error analysis of the enthalpy method for the Stefanproblem. IMA J. Numer. Anal. 7, 61-71 (1987)
7. D. Gilbarg, N. S. Trudinger: Elliptic Partial Differential Equations of Second Order. Grundlehren der Mathematischen Wissenschaften, 224, 2nd ed., Berlin; Springer 1983
8. A. Handlovičová: Error estimates of a linear approximation scheme for nonlinear diffusion problems. Acta Math. Univ. Comenianae 61, 27-39 (1992)
9. W. Jäger, J. Kačur: Solution of porous medium type systems by linear approximation schemes. Numer. Math. 60, 407-427 (1991)
10. 2AN. Math. Model. Numer. Anal. 29, 605-627 (1995)
11. W. Jäger, Y. G. Lu: Hölder continuity of solutions of degenerate parabolic equations, to appear
12. J. W. Jerome: Approximation of Nonlinear Evolution Systems. New York: Academic Press 1983
13. J. Kačur: Solution to strongly nonlinear parabolic problems by a linear approximation scheme. IMA J. Numer. Anal. 19, 119-145 (1999)
14. J. Kačur, A. Handlovičová, M. Kačurová: Solution of nonlinear diffusion problems by linear approximation schemes. SIAM J. Numer. Anal. 30, 1703-1722 (1993)
15. 2AN. Math. Model. Numer. Anal. 21, 655-678 (1987)
16. R. H. Nochetto, C. Verdi: Approximation of degenerate parabolic problems using numerical integration. SIAM J. Numer. Anal.25, 784-814 (1988)
17. O. A. Oleinik, A. S. Kalashnikov, Y.-L. Zhou: The Cauchy problem and boundary value problems for equations of the type of unsteady filtration. Izv. Akad. Nauk SSSR Ser. Mat. 22, 667-704 (1958)
18. 1-contraction and uniqueness for quasilinear elliptic-parabolic equations. J. Differ. Equations 131, 20-38 (1996)
19. I. S. Pop: Regularization methods in the numerical analysis of some degenerate parabolic equations. SFB 359 Preprint 98-43, (1998), IWR, University of Heidelberg
20. J. Rulla: Error analysis for implicit approximations to solutions to Cauchy problems. SIAM J. Numer. Anal. 33, 68-87 (1996)
21. M. Slodička: Solution of nonlinear parabolic problems by linearization. Preprint M3-92, (1992), Comenius University Bratislava, Faculty of Mathematics and Physics
22. V. Thomée: Galerkin Finite Element Methods for Parabolic Problems. Lecture Notes in Math. 1054, Berlin: Springer 1984
23. M. Watanabe: An approach by difference to the porous medium equation with convection. Hiroshima Math. J. 25, 623-645 (1995)
24. W. A. Yong, I. S. Pop: A numerical approach to porous medium equations. SFB-359 Preprint 96-50, (1996), IWR, University of Heidelberg