zbMATH — the first resource for mathematics

Examples
Geometry Search for the term Geometry in any field. Queries are case-independent.
Funct* Wildcard queries are specified by * (e.g. functions, functorial, etc.). Otherwise the search is exact.
"Topological group" Phrases (multi-words) should be set in "straight quotation marks".
au: Bourbaki & ti: Algebra Search for author and title. The and-operator & is default and can be omitted.
Chebyshev | Tschebyscheff The or-operator | allows to search for Chebyshev or Tschebyscheff.
"Quasi* map*" py: 1989 The resulting documents have publication year 1989.
so: Eur* J* Mat* Soc* cc: 14 Search for publications in a particular source with a Mathematics Subject Classification code (cc) in 14.
"Partial diff* eq*" ! elliptic The not-operator ! eliminates all results containing the word elliptic.
dt: b & au: Hilbert The document type is set to books; alternatively: j for journal articles, a for book articles.
py: 2000-2015 cc: (94A | 11T) Number ranges are accepted. Terms can be grouped within (parentheses).
la: chinese Find documents in a given language. ISO 639-1 language codes can also be used.

Operators
a & b logic and
a | b logic or
!ab logic not
abc* right wildcard
"ab c" phrase
(ab c) parentheses
Fields
any anywhere an internal document identifier
au author, editor ai internal author identifier
ti title la language
so source ab review, abstract
py publication year rv reviewer
cc MSC code ut uncontrolled term
dt document type (j: journal article; b: book; a: book article)
Finite difference scheme for variational inequalities. (English) Zbl 0848.49007
Summary: In this paper, we show that a class of variational inequalities related with odd-order obstacle problems can be characterized by a system of differential equations, which are solved using the finite difference scheme. The variational inequality formulation is used to discuss the uniqueness and existence of the solution of the obstacle problems.
MSC:
49J40Variational methods including variational inequalities
References:
[1]Stampacchia, G.,Formes Bilineaires Coercitives sur les Ensembles Convexes, Comptes Rendus de l’Academie des Sciences, Paris, Vol. 258, pp. 4413–4416, 1964.
[2]Noor, M. A., Noor, K. I., andRassias, T. M.,Some Aspects of Variational Inequalities, Journal of Computational and Applied Mathematics, Vol. 47, pp. 285–312, 1993. · Zbl 0788.65074 · doi:10.1016/0377-0427(93)90058-J
[3]Kinderlehrer, D., andStampacchia, G.,An Introduction to Variational Inequalities and Their Applications, Academic Press, New York, New York, 1980.
[4]Cottle, R. W., Giannessi, F., andLions, J. L.,Variational Inequalities and Complementarity Problems, J. Wiley and Sons, New York, New York, 1980.
[5]Glowinski, R., Lions, J. L., andTremolieres, R.,Numerical Analysis of Variational Inequalities, North Holland, Amsterdam, Holland, 1981.
[6]Al-Gwaiz, M. A.,Theory of Distributions, Marcel Dekker, New York, New York, 1992.
[7]Kikuchi, N., andOden, J. T.,Contact Problems in Elasticity, Society for Industrial and Applied Mathematics, Philadelphia, Pennsylvania, 1988.
[8]Noor, M. A.,Wiener-Hopf Equations and Variational Inequalities, Journal of Optimization Theory and Applications, Vol. 79, pp. 197–206, 1994. · Zbl 0799.49010 · doi:10.1007/BF00941894
[9]Noor, M. A.,Variational Inequalities in Physical Oceanography, Ocean Waves Engineering, Edited by M. Rahman, Computational Mechanics Publications, Southampton, England, pp. 201–226, 1994.
[10]Lewy, H., andStampacchia, G.,On the Regularity of the Solutions of the Variational Inequalities, Communication on Pure and Applied Mathematics, Vol. 22, pp. 153–188, 1969. · Zbl 0167.11501 · doi:10.1002/cpa.3160220203
[11]Noor, M. A., andKhalifa, A. K.,Quintic Splines for Solving Contact Problems, Applied Mathematics Letters, Vol. 3, pp. 81–83, 1990. · Zbl 0707.73096 · doi:10.1016/0893-9659(90)90142-X
[12]Noor, M. A., andKhalifa, A. K.,Cubic Splines Collocation Methods for Unilateral Problems, International Journal of Engineering Science, Vol. 25, pp. 1525–1530, 1987. · Zbl 0624.73120 · doi:10.1016/0020-7225(87)90030-9
[13]Noor, M. A., andKhalifa, A. K.,A Numerical Approach for Odd Order Obstacle Problems, International Journal of Computer Mathematics, Vol. 54, pp. 109–116, 1994. · Zbl 0828.65073 · doi:10.1080/00207169408804343
[14]Dunbar, S. R.,Geometric Analysis of Nonlinear Boundary-Value Problems from Physical Oceanography, SIAM Journal on Mathematical Analysis, Vol. 24, pp. 444–465, 1993. · Zbl 0770.34021 · doi:10.1137/0524028
[15]Noor, M. A.,General Variational Inequalities, Applied Mathematics Letters, Vol. 1, pp. 119–122, 1988. · Zbl 0655.49005 · doi:10.1016/0893-9659(88)90054-7