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Page 981 of Mathematical Reviews Vol. , Issue 98B [page]

1998 Mathematical Reviews  
for systems described by variational inequalities with nonlinear operators.  ...  This paper deals with a modified principle of iterative prox- regularization for solving variational problems of the form min{J(u): u € K}, where K is a closed convex subset of a Hilbert space V and J  ... 

Convergence of penalty Robin-Robin domain decomposition methods for unilateral multibody contact problems of elasticity [article]

Ivan I. Dyyak, Ihor I. Prokopyshyn, Ivan A. Prokopyshyn
2015 arXiv   pre-print
These DDMs are based on the penalty method for variational inequalities and some stationary and nonstationary iterative methods for nonlinear variational equations.  ...  The paper is devoted to the penalty Robin-Robin domain decomposition methods (DDMs), proposed by us for the solution of unilateral multibody contact problems of elasticity.  ...  This domain decomposition method in each iteration require to solve linear elasticity problems with Robin boundary conditions for both of the bodies.  ... 
arXiv:1208.6478v2 fatcat:7er3su62f5dwhf53en6cjmd6v4

An Efficient Method for Solving System of Third-Order Nonlinear Boundary Value Problems

Muhammad Noor, Khalida Noor, Asif Waheed, Eisa A. Al-Said
2011 Mathematical Problems in Engineering  
we use the modified variation of parameters method for finding the analytical solution of a system of third-order nonlinear boundary value problems associated with obstacle, unilateral, and contact problems  ...  The results are calculated in terms of convergent series with easily computable components.  ...  Junaid Zaidi, Rector, CIIT for providing the excellent research facilities.  ... 
doi:10.1155/2011/250184 fatcat:vt4umf52hbazflouv445d6mxqq

Meshless numerical analysis of partial differential equations with nonlinear inequality constraints

Mei Chen, Xiaolin Li
2015 Advances in Difference Equations  
This meshless method only requires nodes on the boundary of the domain, and it does not require any numerical integrations.  ...  A meshless method for the numerical solution of partial differential equations with nonlinear inequality constraints is discussed in this paper.  ...  Unfortunately, presumably because nonlinearity and inequation simultaneously exist, the research on meshless methods for problems with nonlinear inequality constraints is scarce.  ... 
doi:10.1186/s13662-015-0514-7 fatcat:cg4hngmaazbyvgrjrdvqj2ygs4

Page 5343 of Mathematical Reviews Vol. , Issue 90I [page]

1990 Mathematical Reviews  
nonlinear variational inequalities.  ...  This type of convergence is applied to study the behaviour of so- lutions of variational inequalities with operators having various domains of definition. B. T.  ... 

Page 5804 of Mathematical Reviews Vol. , Issue 97I [page]

1997 Mathematical Reviews  
In each step of the 73 MECHANICS OF SOLIDS 5804 Kachanov iteration, one has a (linear) variational inequality of the second kind, which can be solved by using a regularization tech- nique.  ...  The authors prove a convergence result for the Kachanov method of solving general nonlinear variational inequalities of the second kind (i.e. these are inequalities because of the pres- ence of non-differentiable  ... 

Page 2827 of Mathematical Reviews Vol. , Issue 94e [page]

1994 Mathematical Reviews  
An iterative method for solving linear operator equations with a spectrum on two segments. (Russian) Trudy Tbiliss. Mat. Inst. Razmadze Akad. Nauk Gruzii 96 (1991), 25-28.  ...  Mikhail Ostrovskii (Khar’kov) 94e:65061 65310 47H17 47H19 49340 65K10 Noor, Muhammad Aslam (SAR-RYADS; Riyadh) Iterative algorithms for nonlinear variational inequalities. (English summary) Panamer.  ... 

Page 6869 of Mathematical Reviews Vol. , Issue 99j [page]

1999 Mathematical Reviews  
This alternative formulation enables him to suggest a number of iterative algorithms for solving variational inequalities. Convergence criteria for these algorithms are studied.  ...  The equations have the form (1) Ax + Tx = 0, where A: ¥ — X* is a bounded linear operator, T = F+G, G:X — X* is a nonlinear operator with dense domain, and Fx = grad f(x) is a bounded nonlinear operator  ... 

Page 7635 of Mathematical Reviews Vol. , Issue 95m [page]

1995 Mathematical Reviews  
The paper deals with elliptic second-order-variational inequalities of obstacle type associated with a bounded domain in the plane.  ...  A finite element method for solving second-order linear elliptic boundary value problems is considered.  ... 

Page 3483 of Mathematical Reviews Vol. , Issue 85h [page]

1985 Mathematical Reviews  
[Finite difference approximation of elliptic variational inequalities with constraints in the domain and on the boundary] Wiss. Z. Tech. Hochsch. Karl-Marz-Stadt 26 (1984), no. 2, 228-234.  ...  Author’s summary: “We investigate finite difference approxima- tions for linear elliptic variational inequalities under boundary con- ditions of the third kind.  ... 

Non-overlapping domain decomposition method for a variational inequality with gradient constraints

A Lapin, E Laitinen, S Lapin
2016 IOP Conference Series: Materials Science and Engineering  
Non-overlapping domain decomposition method is applied to a variational inequality with nonlinear diffusion-convection operator and gradient constraints.  ...  For the resulting constrained saddle point problem block relaxation-Uzawa iterative solution method is applied.  ...  In this article we apply the aforementioned results on the iterative solution methods for the constrained saddle point problems to non-overlapping domain decomposition method for variational inequalities  ... 
doi:10.1088/1757-899x/158/1/012060 fatcat:iihlekhkt5a4diq4a5kk5eus6m

Iterative methods for a class of complementarity problems

Muhammad Aslam Noor
1988 Journal of Mathematical Analysis and Applications  
is a nonlinear transformation from R" into itself.  ...  It is proved that the approximate solution obtained from the iterative scheme converges to the exact solution. Several special cases are also discussed. b 1988 Academic Press. Inc.  ...  Most of these iterative methods are based on the extensions of their counterparts for solving square systems of linear equations.  ... 
doi:10.1016/0022-247x(88)90408-8 fatcat:dncq3knu5ngb3bhdufxh6mazry

Page 1654 of Mathematical Reviews Vol. , Issue 82d [page]

1982 Mathematical Reviews  
The author deals with the nonlinear variational inequality of the second kind: a(u,o—u)+pa(u,v—u)+j(v)—j(u)=(f,vo—u) for all v€V, where a>0, p>0, V=Hj(Q), a(u,v)= fo Vuvodx, (u,v) = fguodx, fEL*(Q), j(  ...  The inequality is approximated by the finite element method with triangular elements and linear interpolating functions.  ... 

Page 3573 of Mathematical Reviews Vol. , Issue 90F [page]

1990 Mathematical Reviews  
The algorithm for time integration combines a fully implicit Adams-Moulton algorithm with the isotherm-Newton method for solving the nonlinear set of differential-algebraic equations that result from the  ...  On i- level nets Q;, i = 2,3,---,/, the unknowns U; at the vertices Q;_; and Uj at the midpoints Q;/Q;_; satisfy block equations, which are solved by block Jacobi, GS and SOR iterations with conver- gence  ... 

Computational Zooming in Near Unilateral Cracks by Schwarz Method with Total Overlap

Faker Ben Belgacem
2019 Journal of Mathematical Study  
This enables users to run one of many efficient algorithms found in the literature to solve the linear macro-problem.  ...  As for the classical Schwarz method, the communication between the micro (local) and macro (global) levels is achieved iteratively through some suitable boundary conditions.  ...  The foundation of the analysis are appropriate variational tools applied to the linear problem on η and to the nonlinear problem on χ.  ... 
doi:10.4208/jms.v52n4.19.02 fatcat:cegedsv24bh2pcvg5h6oi6go3a
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