L ∞ -error estimates for variational inequalities with Hölder continuous obstacle
Finzi Vita, Stefano
ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique, Tome 16 (1982), p. 27-37 / Harvested from Numdam
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@article{M2AN_1982__16_1_27_0,
     author = {Finzi Vita, Stefano},
     title = {$L\_\infty $-error estimates for variational inequalities with H\"older continuous obstacle},
     journal = {ESAIM: Mathematical Modelling and Numerical Analysis - Mod\'elisation Math\'ematique et Analyse Num\'erique},
     volume = {16},
     year = {1982},
     pages = {27-37},
     mrnumber = {648743},
     zbl = {0493.49011},
     language = {en},
     url = {http://dml.mathdoc.fr/item/M2AN_1982__16_1_27_0}
}

Finzi Vita, Stefano. $L_\infty $-error estimates for variational inequalities with Hölder continuous obstacle. ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique, Tome 16 (1982) pp. 27-37. http://gdmltest.u-ga.fr/item/M2AN_1982__16_1_27_0/

1. C Baiocchi, Estimation d’erreur dans L ∞ pour les inéquations à obstacle, Proc.Conf. on « Mathemetical Aspects of Finite Element Method » (Rome, 1975), Lecture Notes in Math., 606 (1977), pp. 27-34. | MR 488847 | Zbl 0374.65053

2. C. Baiocchi and G. A. Pozzi, Error estimates and free-boundary convergence for a finite difference discretization of a parabolic variational inequality, R.A.LR.O., Analyse Numér., 11 (1977), pp. 315-340. | Numdam | MR 464607 | Zbl 0371.65020

3. A. Bensoussan and J. L. Lions, C. R. Acad. Sci Paris, A-276 (1973), pp. 1411-1415, 1189-1192, 1333-1338 ; A-278 (1974), pp. 675-679, 747-751. | Zbl 0264.49006

4. M. Biroli, A De Giorgi-Nash-Moser result for a variational inequality, Boll U.M.I, 16-A (1979), pp. 598-605. | MR 551388 | Zbl 0424.35035

5. H. Brezis, Problèmes unilatéraux, J. Math, pures et appl, 51 (1972), pp. 1-168. | MR 428137 | Zbl 0237.35001

6. F. Brezzi, W. W. Hager and P. A. Raviart , Error estimates for the finite element solution of variational inequalities (Part I), Numer. Math., 28 (1977), pp. 431-443. | MR 448949 | Zbl 0369.65030

7. L. A. Caffarelli and D. Kinderlehrer, Potential methods in variational inequalities, J. Anal Math., 37 (1980), pp. 285-295. | MR 583641 | Zbl 0455.49010

8. M. Chipot, Sur la régularité lipscitzienne de la solution d'inéquations elliptiques, J. Math, pures et appl., 57 (1978), pp. 69-76. | MR 481499 | Zbl 0335.35038

9. P. G. Ciarlet, The finite element method for elliptic problems, North Holland Ed.Amsterdam (1978). | MR 520174 | Zbl 0383.65058

10. P. G. Ciarlet and P. A. Raviart, Maximum principle and uniform convergence for thefinite element method, Comput. Methods Appl. Mech. Engrg., 2 (1973), pp.17-31. | MR 375802 | Zbl 0251.65069

11. P. Cortey Dumont, Approximation numérique d'une inéquation quasi-variationnelle liée à problème de gestion de stock, R.A I.R.O., Analyse Numér., 14 (1980),pp. 335-346. | Numdam | MR 596539 | Zbl 0462.65045

12. J. Frehse, On the smoothness of variational inequalities with obstacle, Proc. Semester on P.D.E., Banach Center, Warszawa (1978).

13. J. Frehse and U. Mosco, Variational inequalities with one-sided irregular obstacles, Manuscripta Math., 28 (1979), pp. 219-233. | MR 535703 | Zbl 0447.49006

14. H. Lewy and G. Stampacchia, On the regularity of the solution of a variational inequality, Comm. Pure Appl. Math., 22 (1969), pp. 153-188. | MR 247551 | Zbl 0167.11501

15. E. Loinger, A finite element approach to a quasi-variational inequality, Calcolo,17 (1980), pp. 197-209. | MR 631586 | Zbl 0458.65060

16.U. Mosco, Implicit variational problems and quasi-variational inequalities, Proc.Summer School on « Nonlinear Operators and the Calculus of Variations » (Bruxelles, 1975), Lecture Notes in Math., 543 (1976), pp. 83-156. | MR 513202 | Zbl 0346.49003

17. J. Nitsche, L ∞ -convergence of finite element approximation, Proc. Conf. on « Mathematical Aspects of Finite Element Methods» (Rome, 1975), Lecture Notes in Math.,606 (1977), pp. 261-274. | MR 488848 | Zbl 0362.65088

18. A. H. Schatz and L. B. Wahlbin, On the quasi-optimality in L ∞ of the H 0 1 -projection into finite element spaces, to appear. | Zbl 0483.65006