L -error estimates for variational inequalities with Hölder continuous obstacle

Stefano Finzi Vita

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique (1982)

  • Volume: 16, Issue: 1, page 27-37
  • ISSN: 0764-583X

How to cite

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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 16.1 (1982): 27-37. <http://eudml.org/doc/193388>.

@article{FinziVita1982,
author = {Finzi Vita, Stefano},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique},
keywords = {variational inequalities; obstacle problems; finite elements; error estimates},
language = {eng},
number = {1},
pages = {27-37},
publisher = {Dunod},
title = {$L_\infty $-error estimates for variational inequalities with Hölder continuous obstacle},
url = {http://eudml.org/doc/193388},
volume = {16},
year = {1982},
}

TY - JOUR
AU - Finzi Vita, Stefano
TI - $L_\infty $-error estimates for variational inequalities with Hölder continuous obstacle
JO - ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique
PY - 1982
PB - Dunod
VL - 16
IS - 1
SP - 27
EP - 37
LA - eng
KW - variational inequalities; obstacle problems; finite elements; error estimates
UR - http://eudml.org/doc/193388
ER -

References

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  1. 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. Zbl0374.65053MR488847
  2. 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. Zbl0371.65020MR464607
  3. 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. Zbl0264.49006
  4. 4. M. BIROLI, A De Giorgi-Nash-Moser result for a variational inequality, Boll U.M.I, 16-A (1979), pp. 598-605. Zbl0424.35035MR551388
  5. 5. H. BREZIS, Problèmes unilatéraux, J. Math, pures et appl, 51 (1972), pp. 1-168. Zbl0237.35001MR428137
  6. 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. Zbl0369.65030MR448949
  7. 7. L. A. CAFFARELLI and D. KINDERLEHRER, Potential methods in variational inequalities, J. Anal Math., 37 (1980), pp. 285-295. Zbl0455.49010MR583641
  8. 8. M. CHIPOT, Sur la régularité lipscitzienne de la solution d'inéquations elliptiques, J. Math, pures et appl., 57 (1978), pp. 69-76. Zbl0335.35038MR481499
  9. 9. P. G. CIARLET, The finite element method for elliptic problems, North Holland Ed.Amsterdam (1978). Zbl0383.65058MR520174
  10. 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. Zbl0251.65069MR375802
  11. 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. Zbl0462.65045MR596539
  12. 12. J. FREHSE, On the smoothness of variational inequalities with obstacle, Proc. Semester on P.D.E., Banach Center, Warszawa (1978). 
  13. 13. J. FREHSE and U. Mosco, Variational inequalities with one-sided irregular obstacles, Manuscripta Math., 28 (1979), pp. 219-233. Zbl0447.49006MR535703
  14. 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. Zbl0167.11501MR247551
  15. 15. E. LOINGER, A finite element approach to a quasi-variational inequality, Calcolo,17 (1980), pp. 197-209. Zbl0458.65060MR631586
  16. 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. Zbl0346.49003MR513202
  17. 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. Zbl0362.65088MR488848
  18. 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. Zbl0483.65006

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