Variational inequalities in Banach spaces
Variational inequalities in noncompact nonconvex regions
In this paper, a general existence theorem on the generalized variational inequality problem GVI(T,C,ϕ) is derived by using our new versions of Nikaidô's coincidence theorem, for the case where the region C is noncompact and nonconvex, but merely is a nearly convex set. Equipped with a kind of V₀-Karamardian condition, this general existence theorem contains some existing ones as special cases. Based on a Saigal condition, we also modify the main theorem to obtain another existence theorem on GVI(T,C,ϕ),...
Variational inequalities in plasticity with strain-hardening - equilibrium finite element approach
The incremental finite element method is applied to find the numerical solution of the plasticity problem with strain-hardening. Following Watwood and Hartz, the stress field is approximated by equilibrium triangular elements with linear functions. The field of the strain-hardening parameter is considered to be piecewise linear. The resulting nonlinear optimization problem with constraints is solved by the Lagrange multipliers method with additional variables. A comparison of the results obtained...
Variational Inequalities with One-Sided Irregular Obstacles.
Variational inequality problems in -spaces.
Variational integrals for elliptic complexes
We discuss variational integrals which are defined on differential forms associated with a given first order elliptic complex. This general framework provides us with better understanding of the concepts of convexity, even in the classical setting
Variational particle schemes for the porous medium equation and for the system of isentropic Euler equations
Both the porous medium equation and the system of isentropic Euler equations can be considered as steepest descents on suitable manifolds of probability measures in the framework of optimal transport theory. By discretizing these variational characterizations instead of the partial differential equations themselves, we obtain new schemes with remarkable stability properties. We show that they capture successfully the nonlinear features of the flows, such as shocks and rarefaction waves for...
Variational Principles and Convergence of Finite Element Approximations of a Holonomic Elastic-Plastic Problem.
Variational Principles for Monotone and Maximal Bifunctions
2000 Mathematics Subject Classification: 49J40, 49J35, 58E30, 47H05We establish variational principles for monotone and maximal bifunctions of Brøndsted-Rockafellar type by using our characterization of bifunction’s maximality in reflexive Banach spaces. As applications, we give an existence result of saddle point for convex-concave function and solve an approximate inclusion governed by a maximal monotone operator.
Variational problems with non-constant gradient constraints.
Variational-hemivariational inequalities in nonlinear elasticity. The coercive case
Existence of a solution of the problem of nonlinear elasticity with non-classical boundary conditions, when the relationship between the corresponding dual quantities is given in terms of a nonmonotone and generally multivalued relation. The mathematical formulation leads to a problem of non-smooth and nonconvex optimization, and in its weak form to hemivariational inequalities and to the determination of the so called substationary points of the given potential.
Variational-like inclusions and resolvent equations involving infinite family of set-valued mappings.
Verification of functional a posteriori error estimates for obstacle problem in 1D
We verify functional a posteriori error estimate for obstacle problem proposed by Repin. Simplification into 1D allows for the construction of a nonlinear benchmark for which an exact solution of the obstacle problem can be derived. Quality of a numerical approximation obtained by the finite element method is compared with the exact solution and the error of approximation is bounded from above by a majorant error estimate. The sharpness of the majorant error estimate is discussed.
Verification of functional a posteriori error estimates for obstacle problem in 2D
We verify functional a posteriori error estimates proposed by S. Repin for a class of obstacle problems in two space dimensions. New benchmarks with known analytical solution are constructed based on one dimensional benchmark introduced by P. Harasim and J. Valdman. Numerical approximation of the solution of the obstacle problem is obtained by the finite element method using bilinear elements on a rectangular mesh. Error of the approximation is measured by a functional majorant. The majorant value...
Weak convergence theorem by an extragradient method for variational inequality, equilibrium and fixed point problems.
Weight minimization of an elastic plate with a unilateral inner obstacle by a mixed finite element method
Unilateral deflection problem of a clamped plate above a rigid inner obstacle is considered. The variable thickness of the plate is to be optimized to reach minimal weight under some constraints for maximal stresses. Since the constraints are expressed in terms of the bending moments only, Herrmann-Hellan finite element scheme is employed. The existence of an optimal thickness is proved and some convergence analysis for approximate penalized optimal design problem is presented.
Wiener--Hopf equations technique for general variational inequalities involving relaxed monotone mappings and nonexpansive mappings.
Выпуклые множества в и их нормальные конусы. Приложения к вариационным неравенствам.
Итерационный метод штрафа для вариационных неравенств с сильно монотонными операторами.
О динамической системе, порожденной двумерными уравнениями движения среды Бингама