Search results for "Variational inequality"

Penalty Function Methods for the Numerical Solution of Nonlinear Obstacle Problems with Finite Elements

2008

A class of penalty function methods for the solution of nonlinear variational inequalities with obstacles ⩽ 0 fur alle v ⩾ ψ in the Sobolev space W1, p (ω) is studied. The (nonlinear) penalty equations are solved by finite element techniques; the order of convergence of this procedure which depends on the regularity of the solution as well as on the finite elements used is investigated. Eine Klasse von Penalty-Methoden zur Losung nichtlinearer Variationsungleichungen mit Hindernisnebenbedingungen ⩽ 0 fur alle v ⩾ ψ im Sobolev Raum W1, p (ω) wird untersucht. Die (nichtlinearen) Penalty-Gleichungen werden mit Hilfe der Finite Elemente Methode gelost; die Konvergenzordnung dieses Verfahrens, w…

Generalized Quasi-Variational Inequalities and Traffic Equilibrium Problem

1995

The model that expresses the traffic equilibrium problem in terms of Quasi-Variational Inequalities is improved taking into account that: i) the cost function may be discontinuous; ii) the cost function may be considered as a multifunction. Existence theorems in such directions are given with examples and considerations, based on a direct computational method, that justify this approach.

Holder continuity of solutions for a class of nonlinear elliptic variational inequalities of high order

2001

A compliant visco-plastic particle contact model based on differential variational inequalities

2013

This work describes an approach to simulate contacts between threedimensional shapes with compliance and damping using the framework of the differential variational inequality theory. Within the context of nonsmooth dynamics, we introduce an extension to the classical set-valued model for frictional contacts between rigid bodies, allowing contacts to experience local compliance, viscosity, and plasticization. Different types of yield surfaces can be defined for various types of contact, a versatile approach that contains the classic dry Coulomb friction as a special case. The resulting problem is a differential variational inequality that can be solved, at each integration time step, as a v…

Irregular Time Dependent Obstacles

2010

Abstract We study the obstacle problem for the Evolutionary p-Laplace Equation when the obstacle is discontinuous and does not have regularity in the time variable. Two quite different procedures yield the same solution.

A simulation function approach for best proximity point and variational inequality problems

2017

We study sufficient conditions for existence of solutions to the global optimization problem min(x is an element of A) d(x, fx), where A, B are nonempty subsets of a metric space (X, d) and f : A -> B belongs to the class of proximal simulative contraction mappings. Our results unify, improve and generalize various comparable results in the existing literature on this topic. As an application of the obtained theorems, we give some solvability theorems of a variational inequality problem.

Shape optimization for Stokes problem with threshold slip boundary conditions

2017

This paper deals with shape optimization of systems governed by the Stokes flow with threshold slip boundary conditions. The stability of solutions to the state problem with respect to a class of domains is studied. For computational purposes the slip term and impermeability condition are handled by a regularization. To get a finite dimensional optimization problem, the optimized part of the boundary is described by B´ezier polynomials. Numerical examples illustrate the computational efficiency. peerReviewed

Biharmonic obstacle problem: guaranteed and computable error bounds for approximate solutions

2020

The paper is concerned with a free boundary problem generated by the biharmonic operator and an obstacle. The main goal is to deduce a fully guaranteed upper bound of the difference between the exact minimizer u and any function (approximation) from the corresponding energy class (which consists of the functions in $H^2$ satisfying the prescribed boundary conditions and the restrictions stipulated by the obstacle). For this purpose we use the duality method of the calculus of variations and general type error identities earlier derived for a wide class of convex variational problems. By this method, we define a combined primal--dual measure of error. It contains four terms of different natu…

Shape optimization in contact problems : Approximation and numerical realization

1987

The optímal shape design of a two-dimensíonal elastic body on rigid foundatíon is analyzed. The relation between the continuous problem and the díscrete problem achieved by FEM is presented. A numerícal realization together wíth the sensítivity analysís is given. Several numerical examples to illustrate the practícal use of the methods are presented. peerReviewed

On the Porosity of Free Boundaries in Degenerate Variational Inequalities

2000

Abstract In this note we consider a certain degenerate variational problem with constraint identically zero. The exact growth of the solution near the free boundary is established. A consequence of this is that the free boundary is porous and therefore its Hausdorff dimension is less than N and hence it is of Lebesgue measure zero.