Geodesic
$L^\infty$-error estimate for a~discrete two-sided obstacle problem and multilevel projective algorithm
Lobachevskii journal of mathematics, Tome 24 (2006), pp. 43-53.

Voir la notice de l'article provenant de la source Math-Net.Ru

We are interested in the approximation in the $L^\infty$-norm of variational inequalities with two-sided obstacle. We show that the order of convergence will be the same as that of variational inequalities with one obstacle. We also give multilevel projective algorithm and discuss its convergence.
Keywords: variational inequalities, $L^\infty$-error estimate, Multilevel projective algorithm. 
@article{LJM_2006_24_a2,
     author = {Y.-J. Jiang and J.-P. Zeng},
     title = {$L^\infty$-error estimate for a~discrete two-sided obstacle problem and multilevel projective algorithm},
     journal = {Lobachevskii journal of mathematics},
     pages = {43--53},
     publisher = {mathdoc},
     volume = {24},
     year = {2006},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/LJM_2006_24_a2/}
}
TY  - JOUR
AU  - Y.-J. Jiang
AU  - J.-P. Zeng
TI  - $L^\infty$-error estimate for a~discrete two-sided obstacle problem and multilevel projective algorithm
JO  - Lobachevskii journal of mathematics
PY  - 2006
SP  - 43
EP  - 53
VL  - 24
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/LJM_2006_24_a2/
LA  - en
ID  - LJM_2006_24_a2
ER  - 
%0 Journal Article
%A Y.-J. Jiang
%A J.-P. Zeng
%T $L^\infty$-error estimate for a~discrete two-sided obstacle problem and multilevel projective algorithm
%J Lobachevskii journal of mathematics
%D 2006
%P 43-53
%V 24
%I mathdoc
%U http://geodesic.mathdoc.fr/item/LJM_2006_24_a2/
%G en
%F LJM_2006_24_a2
Y.-J. Jiang; J.-P. Zeng. $L^\infty$-error estimate for a~discrete two-sided obstacle problem and multilevel projective algorithm. Lobachevskii journal of mathematics, Tome 24 (2006), pp. 43-53. http://geodesic.mathdoc.fr/item/LJM_2006_24_a2/

[1] C. Baiocchi, “Estimation d'Erreur Dans $L^\infty$ pour les Inequations a Obstacle”, Mathematical Aspects of Finite Element Methods, Lect. Notes Math., 606, eds. I. Galligani, E. Magenes, 1977, 27–34 | MR | Zbl

[2] L. Badea, “A Generalization of the Schwarz Alternating Method to an Arbitrary Number of Subdomain”, Numer. Math., 55 (1989), 61–81 | DOI | MR | Zbl

[3] P. G. Ciarlet, Functions de Green Discretes et Principe du Maximum Discret, Ph.D thesis, University of Paris, 1971

[4] Ph. Cortey-Dumont, “On Finite Element Approximation in the $L^\infty$-Norm of Variational Inequalities”, Numer. Math., 47 (1985), 45–57 | DOI | MR | Zbl

[5] S. Finzi-Vita, “$L^\infty$-Error Estimates for Variational Inequalities with Hölder Continuous Obstacle”, RAIRO Anal. Numer., 16 (1982), 27–37 | MR | Zbl

[6] H. Lewy and G. Stampacchia, “On the Regularity of The Solution of Variational Inequality”, Comm. Pure Appl. Math., 22 (1969), 153–188 | DOI | MR | Zbl

[7] J. A. Nitsche, “$L^\infty$-Convergence of Finite Element Approximations”, Mathematical Aspects of Finite Element Methods, Lect. Notes Math., 606, eds. I. Galligani, E. Magenes, 1977, 261–274 | MR | Zbl

[8] R. H. Nochetto,, “Sharp $L^\infty$-Error Estimates for Semilinear Elliptic Problems with Free Boundaries”, Numer. Math., 54 (1988), 243–255 | DOI | MR | Zbl

[9] J. S. Pang and T. Chan, “Iterative Methods for Variational and Complementarity Problems”, Math. Program., 24 (1982), 284–313 | DOI | MR | Zbl

[10] G. Strehlau, “$L^\infty$-Error Estimate for the Numerical Treatment of the Obstacle Problem by the Penalty Method”, Numer. Funct. Anal. Optim., 10 (1989), 185–198 | DOI | MR | Zbl

[11] P. Tarvainen, Block Relaxation Methods for Algebraic Obstacle Problems with $M$-matrices: Theory and Applications, Doctoral Thesis, Jyväskylä: Dept. Math., University of Jyväskylä, 1994 | MR | Zbl

[12] J. P. Zeng and S.Z. Zhou, “On Monotone and Geometric Convergence of Schwarz Methods for Two-sided Obstacle Problems”, SIAM J. Numer. Anal., 35 (1998), 600–616 | DOI | MR | Zbl

[13] Y. M. Zhang, A Monotonicity Principle and L1-Error Bound for a Discrete Obstacle Problem, Technical Report (TR-96-21), University of Chicago, 1996

[14] Y. M. Zhang, “Multilevel Projection Algorithm for Solving Obstacle Problems”, Comput. Math. Appl., 41 (2001), 1505–1513 | DOI | MR | Zbl