Article
Full entry |
PDF
(0.4 MB)
Feedback
PDF
(0.4 MB)
Feedback
Keywords:
degenerate variational inequalities; numerical solution of variational inequalities; free boundary problem; oxygen diffusion problem
degenerate variational inequalities; numerical solution of variational inequalities; free boundary problem; oxygen diffusion problem
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.
References:
[1] H. W. Alt, S. Luckhaus: Quasilinear elliptic-parabolic differential equations. Math. Z. 183 (1983), 311–341. DOI 10.1007/BF01176474 | MR 0706391
[2] J. Cea: Optimisation: Théorie et Algorithmes. Dunod, Paris, 1971. MR 0298892 | Zbl 0211.17402
[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
[4] R. Donat, A. Marquina and V. Martínez: Shooting methods for one-dimensional diffusion-absorption problems. SIAM J. Numer. Anal. 31 (1994), 572–589. DOI 10.1137/0731031 | MR 1276717
[5] G. Duvaut, J.-L. Lions: Les inéquations en mécanique et en physique. Dunod, Paris, 1972. MR 0464857
[6] J. Ekeland, R. Temam: Convex Analysis and Variational Problems. North-Holland, Amsterdam-Oxford, 1976.
[7] R. M. Furzeland: Analysis and computer packages for Stefan problems. Internal report, Oxford University Computing Laboratory (1979).
[8] R. Glowinsky: Numerical Methods for Nonlinear Variational Problems. Springer-Verlag, New York, 1984. MR 0737005
[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. DOI 10.1137/0730087 | MR 1249039
[10] U. Hornung: A parabolic-elliptic variational inequality. Manuscripta Math. 39 (1982), 155–172. DOI 10.1007/BF01165783 | MR 0675536 | Zbl 0502.35055
[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. DOI 10.1051/m2an/1995290506051 | MR 1352864
[12] J. Kačur: Solution to strongly nonlinear parabolic problems by a linear approximation scheme. IMA J. Numer. Anal. 19 (1999), 119–145. DOI 10.1093/imanum/19.1.119 | MR 1670689
Search
Partner of
