| Title:
|
Application of relaxation scheme to degenerate variational inequalities (English) |
| Author:
|
Babušíková, Jela |
| Language:
|
English |
| Journal:
|
Applications of Mathematics |
| ISSN:
|
0862-7940 (print) |
| ISSN:
|
1572-9109 (online) |
| Volume:
|
46 |
| Issue:
|
6 |
| Year:
|
2001 |
| Pages:
|
419-437 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
In this paper we are concerned with the solution of degenerate variational inequalities. To solve this problem numerically, we propose a numerical scheme which is based on the relaxation scheme using non-standard time discretization. The approximate solution on each time level is obtained in the iterative way by solving the corresponding elliptic variational inequalities. The convergence of the method is proved. (English) |
| Keyword:
|
degenerate variational inequalities |
| Keyword:
|
numerical solution of variational inequalities |
| Keyword:
|
free boundary problem |
| Keyword:
|
oxygen diffusion problem |
| MSC:
|
35K85 |
| MSC:
|
35R35 |
| MSC:
|
49J40 |
| MSC:
|
65K10 |
| MSC:
|
65N22 |
| idZBL:
|
Zbl 1061.49004 |
| idMR:
|
MR1865515 |
| DOI:
|
10.1023/A:1013712628500 |
| . |
| Date available:
|
2009-09-22T18:07:53Z |
| Last updated:
|
2020-07-02 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/134476 |
| . |
| Reference:
|
[1] H. W. Alt, S. Luckhaus: Quasilinear elliptic-parabolic differential equations.Math. Z. 183 (1983), 311–341. MR 0706391, 10.1007/BF01176474 |
| Reference:
|
[2] J. Cea: Optimisation: Théorie et Algorithmes.Dunod, Paris, 1971. Zbl 0211.17402, MR 0298892 |
| Reference:
|
[3] J. Crank, R. S. Gupta: A moving boundary problem arising from the diffusion of oxygen in absorbing tissue.J. Inst. Math. Appl. 10 (1972), 19–23. MR 0347105 |
| Reference:
|
[4] R. Donat, A. Marquina and V. Martínez: Shooting methods for one-dimensional diffusion-absorption problems.SIAM J. Numer. Anal. 31 (1994), 572–589. MR 1276717, 10.1137/0731031 |
| Reference:
|
[5] G. Duvaut, J.-L. Lions: Les inéquations en mécanique et en physique.Dunod, Paris, 1972. MR 0464857 |
| Reference:
|
[6] J. Ekeland, R. Temam: Convex Analysis and Variational Problems.North-Holland, Amsterdam-Oxford, 1976. |
| Reference:
|
[7] R. M. Furzeland: Analysis and computer packages for Stefan problems.Internal report, Oxford University Computing Laboratory (1979). |
| Reference:
|
[8] R. Glowinsky: Numerical Methods for Nonlinear Variational Problems.Springer-Verlag, New York, 1984. MR 0737005 |
| Reference:
|
[9] A. Handlovičová, J. Kačur and M. Kačurová: Solution of nonlinear diffusion problems by linear approximation schemes.SIAM J. Numer. Anal. 30 (1993), 1703–1722. MR 1249039, 10.1137/0730087 |
| Reference:
|
[10] U. Hornung: A parabolic-elliptic variational inequality.Manuscripta Math. 39 (1982), 155–172. Zbl 0502.35055, MR 0675536, 10.1007/BF01165783 |
| Reference:
|
[11] W. Jäger, J. Kačur: Solution of doubly nonlinear and degenerate parabolic problems by relaxation schemes.RAIRO Modél. Math. Anal. Numér. 29 (1995), 605–627. MR 1352864, 10.1051/m2an/1995290506051 |
| Reference:
|
[12] J. Kačur: Solution to strongly nonlinear parabolic problems by a linear approximation scheme.IMA J. Numer. Anal. 19 (1999), 119–145. MR 1670689, 10.1093/imanum/19.1.119 |
| . |
